pith. sign in

arxiv: 2604.18192 · v1 · submitted 2026-04-20 · 🧮 math.OC

Local Convergence Results for Sequential Quadratic Programming with Complementarity Constraints

Armin Nurkanovi\'c This is my paper

Pith reviewed 2026-05-10 04:05 UTC · model grok-4.3

classification 🧮 math.OC
keywords local convergenceSQPCCMPCCS-stationary pointsQPCCkappa-omegaactive-set stabilizationsecond-order sufficient conditions
0
0 comments X

The pith

SQPCC converges locally to S-stationary points of MPCCs under weaker second-order conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves a local convergence result for sequential quadratic programming with complementarity constraints (SQPCC) applied to mathematical programs with complementarity constraints (MPCCs). It shows that there exists at least one sequence of S-stationary points from the QPCC subproblems that converges to a reference S-stationary point of the MPCC. The analysis uses the kappa-omega framework to quantify subproblem approximation errors and requires only weaker second-order sufficient conditions at the reference point, without upper-level strict complementarity. This matters because MPCCs violate standard constraint qualifications at every feasible point, so classical SQP applied to reformulations is unreliable, while SQPCC preserves the complementarity structure directly in each subproblem.

Core claim

We show that there exists at least one sequence of QPCC S-stationary points converging to a reference S-stationary point of the MPCC, and we characterize conditions under which each such sequence converges and under which such a sequence is locally unique. In contrast to previous results, the analysis is established under weaker second-order sufficient conditions and requires no upper-level strict complementarity. Our result builds upon local convergence results for the classical SQP method within the kappa-omega setting, which also cover linearly convergent variants. We further establish an active-set stabilization result for SQPCC.

What carries the argument

The kappa-omega setting for quantifying subproblem approximation errors together with weaker second-order sufficient conditions at the reference S-stationary point.

If this is right

  • There exists at least one sequence of QPCC S-stationary points that converges to the reference S-stationary point of the MPCC.
  • Conditions are characterized under which every such sequence converges to the reference point.
  • Conditions are characterized under which the converging sequence is locally unique.
  • The optimal complementarity and inequality active sets are identified after finitely many iterations or only asymptotically, under stated conditions.
  • Local convergence results for classical SQP hold in the kappa-omega setting, including for linearly convergent variants.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The weaker conditions may allow SQPCC to succeed on MPCCs from applications where upper-level strict complementarity does not hold.
  • The same kappa-omega error framework could be applied to analyze convergence of other subproblem-preserving methods for complementarity-constrained problems.
  • Finite active-set stabilization may enable reliable switching to reduced-space methods after identification.
  • The size of the local convergence region can be related explicitly to the degree of nonlinearity through the kappa-omega constants.

Load-bearing premise

The subproblem approximation errors must satisfy the kappa-omega bounds and weaker second-order sufficient conditions must hold at the reference S-stationary point.

What would settle it

A concrete MPCC instance in which the kappa-omega error bounds fail to hold and the SQPCC iterates diverge from the reference S-stationary point, or in which the second-order conditions are violated yet local convergence still occurs.

Figures

Figures reproduced from arXiv: 2604.18192 by Armin Nurkanovi\'c.

Figure 3
Figure 3. Figure 3: The left plot illustrates the iterates of the exact-Hessian SQP method, and the middle plot those of the exact-Hessian SQPCC method in the (w1, w2)-plane. The initial point in both cases is w0 = (0, 2). The right plot shows the errors over the iterations for two methods; the SQPCC method converges to ¯w, and SQP does not. and these are S-stationary points of the corresponding QPCCs. This sequence converges… view at source ↗
read the original abstract

Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible point. This paper analyzes sequential quadratic programming with complementarity constraints (SQPCC). In this method, the complementarity constraints are retained in the subproblems, yielding quadratic programs with complementarity constraints (QPCCs). The main contribution of the paper is a new local convergence result for the SQPCC method to S-stationary points. We show that there exists at least one sequence of QPCC S-stationary points converging to a reference S-stationary point of the MPCC, and we characterize conditions under which each such sequence converges and under which such a sequence is locally unique. In contrast to previous results, the analysis is established under weaker second-order sufficient conditions and requires no upper-level strict complementarity. Our result builds upon local convergence results for the classical SQP method. We present local convergence results for SQP within the kappa-omega setting, which also cover linearly convergent variants. These assumptions, which are widely used in the analysis of Newton-type methods, provide a natural framework for quantifying subproblem approximation errors, their effect on the convergence speed, and the effect of nonlinearity on the size of the local convergence region. Furthermore, we establish an active-set stabilization result for SQPCC, identifying conditions under which the optimal complementarity and inequality active sets are identified after finitely many iterations, and conditions under which such identification occurs only asymptotically. Numerical examples illustrate the theoretical findings and highlight some advantages of SQPCC over classical SQP applied to MPCCs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper analyzes the local convergence of sequential quadratic programming with complementarity constraints (SQPCC) for mathematical programs with complementarity constraints (MPCCs). It establishes that there exists at least one sequence of S-stationary points of the QPCC subproblems converging to a given S-stationary point of the MPCC, and characterizes conditions for convergence and local uniqueness of such sequences. The analysis relies on the kappa-omega framework for quantifying subproblem approximation errors (extending prior SQP results), weaker second-order sufficient conditions at the reference point, and does not require upper-level strict complementarity. Additional results include active-set stabilization (finite or asymptotic identification of active sets) and numerical examples comparing SQPCC to standard SQP on MPCCs.

Significance. If the central convergence claims hold, this work provides a meaningful extension of local SQP theory to the QPCC setting for MPCCs, relaxing prior assumptions on second-order conditions and strict complementarity. The kappa-omega error framework is a strength, as it naturally handles linearly convergent variants and quantifies the impact of nonlinearity on the convergence basin. This could broaden the reliable use of SQPCC in applications involving complementarity, such as mechanics and game theory. The active-set stabilization result is a useful practical addition. Numerical examples are mentioned as validation but do not appear to serve as independent verification of the rates or uniqueness claims.

major comments (2)
  1. The central existence and uniqueness claims in the abstract rely on the kappa-omega error bounds and weaker SOSC at the reference S-stationary point, but the manuscript does not appear to provide explicit derivations of the error bounds for the QPCC subproblems (as opposed to standard QP subproblems). Without these, it is difficult to verify that the approximation errors remain controlled under the weaker SOSC.
  2. Section on active-set stabilization: the conditions for finite vs. asymptotic identification are stated, but it is unclear how they interact with the local uniqueness result for the sequence of QPCC S-stationary points. If the active sets stabilize only asymptotically, this may affect the claimed local uniqueness in a neighborhood.
minor comments (2)
  1. The numerical examples are referenced but lack sufficient detail on problem instances, iteration counts, or observed convergence rates to independently support the theoretical claims.
  2. Notation for the kappa-omega parameters and the S-stationarity definitions should be cross-referenced more explicitly between the SQP background section and the QPCC extension.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: The central existence and uniqueness claims in the abstract rely on the kappa-omega error bounds and weaker SOSC at the reference S-stationary point, but the manuscript does not appear to provide explicit derivations of the error bounds for the QPCC subproblems (as opposed to standard QP subproblems). Without these, it is difficult to verify that the approximation errors remain controlled under the weaker SOSC.

    Authors: We appreciate this observation. Section 3 extends the kappa-omega framework to SQPCC and derives the relevant error bounds for the QPCC subproblems, using the weaker SOSC to control the terms without upper-level strict complementarity. However, we agree the derivations could be more explicit. In the revision we will expand the proof of Theorem 3.2 with additional intermediate steps that isolate the QPCC-specific error contributions and show they remain bounded under the stated assumptions. revision: yes

  2. Referee: Section on active-set stabilization: the conditions for finite vs. asymptotic identification are stated, but it is unclear how they interact with the local uniqueness result for the sequence of QPCC S-stationary points. If the active sets stabilize only asymptotically, this may affect the claimed local uniqueness in a neighborhood.

    Authors: Thank you for noting this interaction. The local uniqueness result (Theorem 4.3) is proved for sequences whose active sets are eventually fixed, while the asymptotic-identification case yields uniqueness only in the limit. We will add a short remark after Theorem 4.3 clarifying that, under asymptotic stabilization, uniqueness holds with respect to the limit point rather than in a fixed neighborhood, and we will adjust the theorem statement accordingly for precision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; extension of prior SQP results with new QPCC arguments

full rationale

The paper extends classical SQP local convergence results (in the kappa-omega framework) to the QPCC subproblem setting for MPCCs. The central claim—existence of sequences of QPCC S-stationary points converging to a reference MPCC S-stationary point, plus conditions for convergence and local uniqueness—relies on weaker SOSC and error bounds without reducing to a self-definition, fitted parameter renamed as prediction, or load-bearing self-citation chain. No equations or steps in the provided abstract and structure equate the target result to its inputs by construction. This is a standard honest extension with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard second-order sufficient conditions at S-stationary points and the kappa-omega error framework from Newton-method analysis; no free parameters are fitted and no new entities are postulated.

axioms (2)
  • domain assumption Weaker second-order sufficient conditions hold at the reference S-stationary point
    Invoked to guarantee local convergence of the QPCC subproblem solutions; appears in the statement of the main result.
  • standard math Kappa-omega framework quantifies subproblem approximation errors
    Used to bound the effect of nonlinearity and approximation quality on the convergence region and rate; referenced as the setting for the SQP analysis.

pith-pipeline@v0.9.0 · 5586 in / 1492 out tokens · 36383 ms · 2026-05-10T04:05:16.174779+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

63 extracted references · 2 canonical work pages · 1 internal anchor

  1. [1]

    Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications.Mathematical Programming, 114:69–99, 2008

    Wolfgang Achtziger and Christian Kanzow. Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications.Mathematical Programming, 114:69–99, 2008

    2008

  2. [2]

    J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl. CasADi – a software framework for nonlinear optimization and optimal control.Mathematical Programming Computation, 11(1):1–36, 2019

    2019

  3. [3]

    Consensus complementarity control for multi-contact mpc.IEEE Transactions on Robotics, 2024

    Alp Aydinoglu, Adam Wei, Wei-Cheng Huang, and Michael Posa. Consensus complementarity control for multi-contact mpc.IEEE Transactions on Robotics, 2024

    2024

  4. [4]

    On convex quadratic programs with linear complementarity constraints

    Lijie Bai, John E Mitchell, and Jong-Shi Pang. On convex quadratic programs with linear complementarity constraints. Computational Optimization and Applications, 54(3):517–554, 2013

    2013

  5. [5]

    Biegler.Nonlinear Programming

    Lorenz T. Biegler.Nonlinear Programming. MOS-SIAM Series on Optimization. SIAM, 2010

    2010

  6. [6]

    H. G. Bock, M. Diehl, E. A. Kostina, and J. P. Schl¨ oder. Constrained optimal feedback control of systems governed by large differential algebraic equations. InReal-Time and Online PDE-Constrained Optimization, pages 3–22. SIAM, 2007. Local Convergence Results for Sequential Quadratic Programming with Complementarity Constraints 25

    2007

  7. [7]

    Bock.Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, volume 183 ofBonner Mathematische Schriften

    H.G. Bock.Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, volume 183 ofBonner Mathematische Schriften. Universit¨ at Bonn, Bonn, 1987

    1987

  8. [8]

    J.F. Bonnans. Local Analysis of Newton-Type Methods for Variational Inequalities and Nonlinear Programming.Appl. Math. Optim, 29:161–186, 1994

    1994

  9. [9]

    Chen and D

    L. Chen and D. Goldfarb. An active set method for mathematical programs with linear complementarity constraint. SIAM Journal on Optimization, 2007. (submitted)

    2007

  10. [10]

    A condensing approach for linear-quadratic optimization with geometric constraints

    Alberto De Marchi. A condensing approach for linear-quadratic optimization with geometric constraints.arXiv preprint arXiv:2510.17465, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  11. [11]

    Constrained composite optimization and augmented lagrangian methods.Mathematical Programming, 201(1):863–896, 2023

    Alberto De Marchi, Xiaoxi Jia, Christian Kanzow, and Patrick Mehlitz. Constrained composite optimization and augmented lagrangian methods.Mathematical Programming, 201(1):863–896, 2023

    2023

  12. [12]

    Springer, 2011

    Peter Deuflhard.Newton methods for nonlinear problems: affine invariance and adaptive algorithms, volume 35. Springer, 2011

    2011

  13. [13]

    Diehl.Real-Time Optimization for Large Scale Nonlinear Processes

    M. Diehl.Real-Time Optimization for Large Scale Nonlinear Processes. PhD thesis, University of Heidelberg, 2001

    2001

  14. [14]

    An adjoint-based SQP algorithm with quasi- Newton Jacobian updates for inequality constrained optimization.Optimization Methods and Software, 25(4):531–552, 2010

    Moritz Diehl, Andrea Walther, Hans Georg Bock, and Ekaterina Kostina. An adjoint-based SQP algorithm with quasi- Newton Jacobian updates for inequality constrained optimization.Optimization Methods and Software, 25(4):531–552, 2010

    2010

  15. [15]

    Complementarity formulations of ℓ0-norm optimization.Pacific Journal of Optimization, 14(2):273–305, 2018

    Mingbin Feng, John J Mitchell, Jong Shi Pang, Xin Shen, and Andreas Waechter. Complementarity formulations of ℓ0-norm optimization.Pacific Journal of Optimization, 14(2):273–305, 2018

    2018

  16. [16]

    H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl. qpOASES: a parametric active-set algorithm for quadratic programming.Mathematical Programming Computation, 6(4):327–363, 2014

    2014

  17. [17]

    Fiacco.Introduction to sensitivity and stability analysis in nonlinear programming

    A.V. Fiacco.Introduction to sensitivity and stability analysis in nonlinear programming. Academic Press, New York, 1983

    1983

  18. [18]

    Fletcher, S

    R. Fletcher, S. Leyffer, D. Ralph, and S. Scholtes. Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints.SIAM Journal on Optimization, 17:259–286, 2006

    2006

  19. [19]

    Multiplier convergence in trust-region methods with application to conver- gence of decomposition methods for mpecs.Mathematical Programming, 112(2):335–369, 2008

    Giovanni Giallombardo and Daniel Ralph. Multiplier convergence in trust-region methods with application to conver- gence of decomposition methods for mpecs.Mathematical Programming, 112(2):335–369, 2008

    2008

  20. [20]

    Lei Guo and Zhibin Deng. A new augmented lagrangian method for mpccs—theoretical and numerical comparison with existing augmented lagrangian methods.Mathematics of Operations Research, 47(2):1229–1246, 2022

    2022

  21. [21]

    LCQPow: a solver for linear complementarity quadratic programs.Mathematical Programming Computation, 2024

    Jonas Hall, Armin Nurkanovi´ c, Florian Messerer, and Moritz Diehl. LCQPow: a solver for linear complementarity quadratic programs.Mathematical Programming Computation, 2024

    2024

  22. [22]

    Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints.Mathematical Programming, 137(1):257–288, 2013

    Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz. Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints.Mathematical Programming, 137(1):257–288, 2013

    2013

  23. [23]

    A note on sensitivity of value functions of mathematical programs with complementarity constraints.Mathematical Programming, 93(2):265–279, 2002

    Xinmin Hu and Daniel Ralph. A note on sensitivity of value functions of mathematical programs with complementarity constraints.Mathematical Programming, 93(2):265–279, 2002

    2002

  24. [24]

    An active-set newton method for mathematical programs with complemen- tarity constraints.SIAM Journal on Optimization, 19(3):1003–1027, 2008

    Alexey F Izmailov and Mikhail V Solodov. An active-set newton method for mathematical programs with complemen- tarity constraints.SIAM Journal on Optimization, 19(3):1003–1027, 2008

    2008

  25. [25]

    Izmailov and Mikhail V

    Alexey F. Izmailov and Mikhail V. Solodov.Newton-Type Methods for Optimization and Variational Problems. Springer, 1 edition, 2014

    2014

  26. [26]

    Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints

    J Ye Jane. Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. Journal of Mathematical Analysis and Applications, 307(1):350–369, 2005

    2005

  27. [27]

    An augmented lagrangian method for optimiza- tion problems with structured geometric constraints.Mathematical Programming, 199(1):1365–1415, 2023

    Xiaoxi Jia, Christian Kanzow, Patrick Mehlitz, and Gerd Wachsmuth. An augmented lagrangian method for optimiza- tion problems with structured geometric constraints.Mathematical Programming, 199(1):1365–1415, 2023

    2023

  28. [28]

    A new regularization scheme for mathematical programs with complementarity constraints.SIAM Journal on Optimization, 20(1):78–103, 2009

    Abdeslam Kadrani, Jean-Pierre Dussault, and Abdelhamid Benchakroun. A new regularization scheme for mathematical programs with complementarity constraints.SIAM Journal on Optimization, 20(1):78–103, 2009

    2009

  29. [29]

    A new regularization method for mathematical programs with comple- mentarity constraints with strong convergence properties.SIAM Journal on Optimization, 23(2):770–798, 2013

    Christian Kanzow and Alexandra Schwartz. A new regularization method for mathematical programs with comple- mentarity constraints with strong convergence properties.SIAM Journal on Optimization, 23(2):770–798, 2013

    2013

  30. [30]

    Christian Kanzow and Alexandra Schwartz. The price of inexactness: convergence properties of relaxation methods for mathematical programs with complementarity constraints revisited.Mathematics of Operations Research, 40(2):253– 275, 2015

    2015

  31. [31]

    The sparse (st) optimization problem: Reformulations, opti- mality, stationarity, and numerical results.Computational Optimization and Applications, pages 1–36, 2024

    Christian Kanzow, Alexandra Schwartz, and Felix Weiß. The sparse (st) optimization problem: Reformulations, opti- mality, stationarity, and numerical results.Computational Optimization and Applications, pages 1–36, 2024

    2024

  32. [32]

    Mpec methods for bilevel optimization problems

    Youngdae Kim, Sven Leyffer, and Todd Munson. Mpec methods for bilevel optimization problems. InBilevel Opti- mization, pages 335–360. Springer, 2020

    2020

  33. [33]

    PhD thesis, Uni- versity of Heidelberg, 2010

    Christian Kirches.Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control. PhD thesis, Uni- versity of Heidelberg, 2010

    2010

  34. [34]

    Sequential linearization method for bound-constrained mathematical programs with complementarity constraints.SIAM Journal on Optimization, 32(1):75–99, 2022

    Christian Kirches, Jeffrey Larson, Sven Leyffer, and Paul Manns. Sequential linearization method for bound-constrained mathematical programs with complementarity constraints.SIAM Journal on Optimization, 32(1):75–99, 2022

    2022

  35. [35]

    Kouzoupis, G

    D. Kouzoupis, G. Frison, A. Zanelli, and M. Diehl. Recent advances in quadratic programming algorithms for nonlinear model predictive control.Vietnam Journal of Mathematics, 46(4):863–882, 2018

    2018

  36. [36]

    A globally convergent filter method for mpecs.Preprint ANL/MCS-P1457-0907, Argonne National Laboratory, Mathematics and Computer Science Division, 2007

    Sven Leyffer and Todd S Munson. A globally convergent filter method for mpecs.Preprint ANL/MCS-P1457-0907, Argonne National Laboratory, Mathematics and Computer Science Division, 2007

    2007

  37. [37]

    Hybrid approach with active set identification for mathematical programs with complementarity constraints.Journal of optimization theory and applications, 128(1):1–28, 2006

    Gui-Hua Lin and Masao Fukushima. Hybrid approach with active set identification for mathematical programs with complementarity constraints.Journal of optimization theory and applications, 128(1):1–28, 2006

    2006

  38. [38]

    Z. Luo, J. Pang, and D. Ralph.Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, 1996

    1996

  39. [39]

    Nocedal and S

    J. Nocedal and S. J. Wright.Numerical Optimization. Springer Series in Operations Research and Financial Engineering. Springer, 2 edition, 2006

    2006

  40. [40]

    PhD thesis, University of Freiburg, 2023

    Armin Nurkanovi´ c.Numerical Methods for Optimal Control of Nonsmooth Dynamical Systems. PhD thesis, University of Freiburg, 2023

    2023

  41. [41]

    NOSNOC: A software package for numerical optimal control of nonsmooth systems.IEEE Control Systems Letters, 6:3110–3115, 2022

    Armin Nurkanovi´ c and Moritz Diehl. NOSNOC: A software package for numerical optimal control of nonsmooth systems.IEEE Control Systems Letters, 6:3110–3115, 2022

    2022

  42. [42]

    FESD-J: Finite elements with switch detection for numerical optimal control of rigid bodies with impacts and coulomb friction.Nonlinear Analysis: Hybrid Systems, 52:101460, 2024

    Armin Nurkanovi´ c, Jonathan Frey, Anton Pozharskiy, and Moritz Diehl. FESD-J: Finite elements with switch detection for numerical optimal control of rigid bodies with impacts and coulomb friction.Nonlinear Analysis: Hybrid Systems, 52:101460, 2024. 26 Armin Nurkanovi´ c

    2024

  43. [43]

    Nurkanovi \'c and S

    Armin Nurkanovi´ c and Sven Leyffer. A globally convergent method for computing b-stationary points of mathematical programs with equilibrium constraints.arXiv preprint arXiv:2501.13835, 2025

    work page arXiv 2025

  44. [44]

    Solving mathematical programs with complementarity con- straints arising in nonsmooth optimal control.Vietnam Journal of Mathematics, pages 1–39, 2024

    Armin Nurkanovi´ c, Anton Pozharskiy, and Moritz Diehl. Solving mathematical programs with complementarity con- straints arising in nonsmooth optimal control.Vietnam Journal of Mathematics, pages 1–39, 2024

    2024

  45. [45]

    Real-time algorithms for model predictive control of hybrid dynamical systems.arXiv preprint, 2026

    Armin Nurkanovi´ c, Anton Pozharskiy, and Moritz Diehl. Real-time algorithms for model predictive control of hybrid dynamical systems.arXiv preprint, 2026

    2026

  46. [46]

    J.V. Outrata. Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints.Math. Oper. Res., 24(3):627–644, 1999

    1999

  47. [47]

    A direct method for trajectory optimization of rigid bodies through contact.The International Journal of Robotics Research, 33(1):69–81, 2014

    Michael Posa, Cecilia Cantu, and Russ Tedrake. A direct method for trajectory optimization of rigid bodies through contact.The International Journal of Robotics Research, 33(1):69–81, 2014

    2014

  48. [48]

    CCOpt: an open-source solver for large-scale mathematical programs with complementarity constraints.arXiv preprint, 2026

    Anton Pozharskiy, Fran¸ cois Pacaud, Moritz Diehl, and Armin Nurkanovi´ c. CCOpt: an open-source solver for large-scale mathematical programs with complementarity constraints.arXiv preprint, 2026

    2026

  49. [49]

    An interior point method for mathematical programs with complemen- tarity constraints (mpccs).SIAM Journal on Optimization, 15(3):720–750, 2005

    Arvind U Raghunathan and Lorenz T Biegler. An interior point method for mathematical programs with complemen- tarity constraints (mpccs).SIAM Journal on Optimization, 15(3):720–750, 2005

    2005

  50. [50]

    Daniel Ralph and Stephen J. Wright. Some properties of regularization and penalization schemes for mpecs.Optimiza- tion Methods and Software, 19(5):527–556, 2004

    2004

  51. [51]

    J. B. Rawlings, D. Q. Mayne, and M. M. Diehl.Model Predictive Control: Theory, Computation, and Design. Nob Hill, 2nd edition, 2017

    2017

  52. [52]

    Optimal power flow with complementarity constraints

    William Rosehart, Codruta Roman, and Antony Schellenberg. Optimal power flow with complementarity constraints. IEEE Transactions on Power Systems, 20(2):813–822, 2005

    2005

  53. [53]

    Scheel and S

    H. Scheel and S. Scholtes. Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity.Math. Oper. Res., 25:1–22, 2000

    2000

  54. [54]

    Convergence properties of a regularization scheme for mathematical programs with complementarity constraints.SIAM Journal on Optimization, 11(4):918–936, 2001

    Stefan Scholtes. Convergence properties of a regularization scheme for mathematical programs with complementarity constraints.SIAM Journal on Optimization, 11(4):918–936, 2001

    2001

  55. [55]

    Nonconvex structures in nonlinear programming.Operations Research, 52(3):368–383, 2004

    Stefan Scholtes. Nonconvex structures in nonlinear programming.Operations Research, 52(3):368–383, 2004

    2004

  56. [56]

    Exact penalization of mathematical programs with equilibrium constraints.SIAM Journal on Control and Optimization, 37(2):617–652, 1999

    Stefan Scholtes and Michael St¨ ohr. Exact penalization of mathematical programs with equilibrium constraints.SIAM Journal on Control and Optimization, 37(2):617–652, 1999

    1999

  57. [57]

    A new relaxation scheme for mathematical programs with equilibrium constraints

    Sonja Steffensen and Michael Ulbrich. A new relaxation scheme for mathematical programs with equilibrium constraints. SIAM Journal on Optimization, 20(5):2504–2539, 2010

    2010

  58. [58]

    Tran-Dinh, C

    Q. Tran-Dinh, C. Savorgnan, and M. Diehl. Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization.SIAM J. Optimization, 22(4):1258–1284, 2012

    2012

  59. [59]

    Exploiting convexity in direct optimal control: a sequential convex quadratic programming method

    Robin Verschueren, Niels van Duijkeren, Rien Quirynen, and Moritz Diehl. Exploiting convexity in direct optimal control: a sequential convex quadratic programming method. InProceedings of the IEEE Conference on Decision and Control (CDC), 2016

    2016

  60. [60]

    On LICQ and the uniqueness of lagrange multipliers.Operations Research Letters, 41(1):78–80, 2013

    Gerd Wachsmuth. On LICQ and the uniqueness of lagrange multipliers.Operations Research Letters, 41(1):78–80, 2013

    2013

  61. [61]

    Andreas W¨ achter and Lorenz T. Biegler. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming.Mathematical Programming, 106(1):25–57, 2006

    2006

  62. [62]

    Superlinear convergence of a stabilized sqp method to a degenerate solution.Computational Optimization and Applications, 11:253–275, 1998

    Stephen J Wright. Superlinear convergence of a stabilized sqp method to a degenerate solution.Computational Optimization and Applications, 11:253–275, 1998

    1998

  63. [63]

    PhD thesis, University of Freiburg, 2021

    Andrea Zanelli.Inexact methods for nonlinear model predictive control: stability, applications, and software. PhD thesis, University of Freiburg, 2021

    2021