pith. sign in

arxiv: 2604.19100 · v1 · submitted 2026-04-21 · 📡 eess.SY · cs.SY

Automated Synthesis of Hardware-implementable Analog Circuits for Constrained Optimization

Sachin Khoja , Kamlesh Sawant , Palak Jain , Sairaj Dhople , Jason Poon This is my paper

Pith reviewed 2026-05-10 02:23 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords analog circuit synthesisconstrained optimizationKKT conditionsSPICE netlisthardware implementationnonlinear optimizationoperational amplifiersscalability
0
0 comments X

The pith

Software automatically designs analog circuits that solve large constrained optimization problems in hardware.

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

The paper describes a software system that takes descriptions of optimization problems and turns them into electronic circuits built from basic parts like amplifiers and capacitors. These circuits are designed so their natural behavior finds the best solution by following the rules for optimality in continuous time. This matters because analog circuits can potentially handle much bigger problems faster than computers that process one step at a time, due to their parallel nature. The system supports problems with nonlinear goals and certain types of limits, and it has been tested on problems with thousands of variables showing big gains in size and speed.

Core claim

The authors show that an automated process can map the variables of an optimization problem to voltages on capacitors and wire up a circuit using operational amplifiers, resistors, capacitors, diodes, and multipliers so that the circuit's evolution satisfies the Karush-Kuhn-Tucker conditions for the optimal solution.

What carries the argument

The mapping of optimization variables to capacitor voltages combined with analog circuit elements that enforce the Karush-Kuhn-Tucker optimality conditions.

Load-bearing premise

That the continuous-time dynamics of the analog circuit will drive the system to the optimal solution even when real components have limitations such as finite speed and noise, and that computer simulations accurately predict the behavior of the physical circuit.

What would settle it

Measuring the output voltages of a physically built version of one synthesized circuit while solving a known optimization problem and checking if it reaches the correct optimal values within the predicted time.

Figures

Figures reproduced from arXiv: 2604.19100 by Jason Poon, Kamlesh Sawant, Palak Jain, Sachin Khoja, Sairaj Dhople.

Figure 1
Figure 1. Figure 1: Circuit schematic for the augmented Lagrangian method to solve the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the automated software toolchain flow. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Analog solver speed comparison with IPOPT solver. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Analog solver speed-accuracy trade-off with IPOPT solver. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

This paper presents an automated software toolchain for synthesizing hardware-implementable analog circuits that solve constrained optimization problems. The proposed toolchain supports nonlinear objective functions with linear and quadratic constraints. It maps optimization variables to capacitor voltages, implementing dynamics that enforce Karush-Kuhn-Tucker conditions using operational amplifiers, resistors, capacitors, diodes, and analog multipliers. From high-level problem descriptions in AMPL or MPS, the toolchain generates a SPICE netlist for the analog circuit, simulates it, and verifies that the solutions converge. The projected settling time of the analog circuit depends on circuit parameters, gain-bandwidth product, and slew-rate limits of operational amplifiers, and leverages the inherent parallelism of analog circuits. The proposed toolchain successfully generates circuits with up to 10,000 variables and demonstrates large scalability improvements, achieving up to a 1,000X increase in solvable problem size over prior analog hardware demonstrations. Simulation studies further show that the automatically synthesized circuits converge to optimal solutions, achieving more than a 200X speedup compared to IPOPT, a state-of-the-art digital interior-point solver.

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 manuscript presents an automated toolchain that converts constrained nonlinear optimization problems specified in AMPL or MPS into SPICE netlists for analog circuits. Variables are mapped to capacitor voltages and dynamics are realized with op-amps, resistors, capacitors, diodes, and multipliers to enforce the KKT conditions; the toolchain then simulates the resulting circuits and reports convergence. It claims successful generation of circuits with up to 10,000 variables (a 1,000X increase over prior analog hardware demonstrations) and more than 200X speedup versus IPOPT in simulations that incorporate gain-bandwidth and slew-rate limits.

Significance. If the simulation results accurately predict physical behavior, the automated synthesis flow would constitute a substantial advance in analog optimization hardware by removing manual circuit design as a bottleneck and demonstrating practical scalability to problem sizes far beyond previous analog demonstrations. The explicit use of KKT-enforcing dynamics and the handling of quadratic constraints are technically noteworthy strengths.

major comments (2)
  1. [Abstract and Simulation Studies] Abstract and Simulation Studies section: while the text states that gain-bandwidth product and slew-rate limits are incorporated for settling-time projection, no quantitative metrics are supplied for solution error, convergence failure rate, or trajectory deviation between ideal and non-ideal component models at the 10,000-variable scale. This comparison is load-bearing for the central claim that the synthesized circuits enforce the KKT conditions and deliver the reported speedups under realistic hardware conditions.
  2. [Results] Results on scalability: the 1,000X increase in solvable problem size is asserted on the basis of successful SPICE netlist generation and simulation, yet the manuscript provides no explicit scaling analysis (e.g., circuit element count versus number of variables or constraints, or memory/time requirements of the netlist generator) that would substantiate the claim beyond the single 10k-variable data point.
minor comments (2)
  1. [Abstract] The abstract reports a 'more than 200X speedup' without stating the specific problem dimensions, constraint types, or number of Monte-Carlo runs used for the IPOPT comparison; adding these details would improve reproducibility.
  2. Figure captions and circuit diagrams would benefit from explicit labeling of the KKT-enforcing sub-circuits (e.g., the multiplier and diode blocks) to make the mapping from optimization formulation to hardware clearer.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive review. The comments highlight important aspects of our claims regarding simulation fidelity and scalability evidence. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract and Simulation Studies] Abstract and Simulation Studies section: while the text states that gain-bandwidth product and slew-rate limits are incorporated for settling-time projection, no quantitative metrics are supplied for solution error, convergence failure rate, or trajectory deviation between ideal and non-ideal component models at the 10,000-variable scale. This comparison is load-bearing for the central claim that the synthesized circuits enforce the KKT conditions and deliver the reported speedups under realistic hardware conditions.

    Authors: We acknowledge that the manuscript does not provide explicit quantitative metrics (e.g., solution error norms, convergence failure rates across runs, or trajectory deviation statistics) comparing ideal versus non-ideal component models specifically at the 10,000-variable scale. The reported simulations were performed in SPICE using models that include finite gain-bandwidth products and slew-rate limits, and the circuits were observed to converge to the known optimal solutions within the projected settling times. To address the concern, we will add a dedicated subsection with tables reporting these metrics for the largest instances, including maximum absolute errors relative to the IPOPT reference solutions and success rates over repeated simulations with varied initial conditions. revision: yes

  2. Referee: [Results] Results on scalability: the 1,000X increase in solvable problem size is asserted on the basis of successful SPICE netlist generation and simulation, yet the manuscript provides no explicit scaling analysis (e.g., circuit element count versus number of variables or constraints, or memory/time requirements of the netlist generator) that would substantiate the claim beyond the single 10k-variable data point.

    Authors: The 1,000X scalability claim rests on the toolchain's successful automatic generation and SPICE simulation of a 10,000-variable circuit (versus prior manual analog designs limited to roughly 10 variables). We agree that an explicit scaling analysis would provide stronger substantiation. In the revised manuscript we will include additional figures and tables that plot the number of circuit elements (op-amps, multipliers, resistors, capacitors) and the netlist generator's runtime and memory usage as functions of problem size, for instances ranging from 100 to 10,000 variables, thereby documenting the scaling behavior beyond the single data point. revision: yes

Circularity Check

0 steps flagged

No circularity: toolchain mapping and SPICE results are independent outputs

full rationale

The paper's central contribution is an automated toolchain that translates AMPL/MPS problem descriptions into SPICE netlists implementing KKT-enforcing analog dynamics via op-amps, multipliers, and diodes. Scalability claims (up to 10k variables, 1000X scale-up) and performance claims (200X speedup vs IPOPT) are obtained directly from running those generated netlists in simulation; they are not fitted parameters renamed as predictions, nor do they reduce to self-citations or prior ansatzes by construction. The mapping itself is an explicit engineering translation whose correctness is checked by simulation rather than assumed tautologically. No load-bearing step equates a result to its own input definition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard optimization theory and analog circuit implementation principles with no new postulated entities or fitted parameters introduced by the paper.

axioms (1)
  • standard math Karush-Kuhn-Tucker (KKT) conditions are necessary for optimality in constrained nonlinear optimization problems.
    The circuit dynamics are designed to enforce KKT conditions as stated in the abstract.

pith-pipeline@v0.9.0 · 5500 in / 1446 out tokens · 54799 ms · 2026-05-10T02:23:44.699467+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

36 extracted references · 36 canonical work pages

  1. [1]

    Boyd and L

    S. Boyd and L. Vandenberghe,Convex Optimization. Cambridge, UK: Cambridge University Press, 2004

    work page 2004

  2. [2]

    Power systems without fuel,

    J. A. Taylor, S. V . Dhople, and D. S. Callaway, “Power systems without fuel,”Renewable and Sustainable Energy Reviews, vol. 57, pp. 1322– 1336, 2016

    work page 2016

  3. [3]

    J. R. R. A. Martins and A. Ning,Engineering Design Optimization. Cambridge: Cambridge University Press, 2021

    work page 2021

  4. [4]

    A survey of neurodynamic optimization,

    Y . Xia, Q. Liu, J. Wang, and A. Cichocki, “A survey of neurodynamic optimization,”IEEE Trans. Emerg. Top. Comput. Intell., vol. 8, no. 4, pp. 2677–2696, 2024

    work page 2024

  5. [5]

    Analog optical computer for AI inference and combinatorial optimization,

    K. P. Kalinin, J. Gladrow, J. Chu, and et al., “Analog optical computer for AI inference and combinatorial optimization,”Nature, vol. 645, pp. 354–361, Sep. 2025

    work page 2025

  6. [6]

    Implementation aspects of model predictive control for embedded systems,

    P. Zometa, M. K ¨ogel, T. Faulwasser, and R. Findeisen, “Implementation aspects of model predictive control for embedded systems,” inProc. Amer. Control Conf., 2012, pp. 1205–1210

    work page 2012

  7. [7]

    Model predictive control of power electronic systems: Methods, results, and challenges,

    P. Karamanakos, E. Liegmann, T. Geyer, and R. Kennel, “Model predictive control of power electronic systems: Methods, results, and challenges,”IEEE Open J. Ind. Appl., vol. 1, pp. 95–114, 2020

    work page 2020

  8. [8]

    Analog optimization circuit for embedded model predictive control,

    A. A. Adegbege and F. D. Moran, “Analog optimization circuit for embedded model predictive control,”IEEE Trans. Circuits Syst. I Reg. Papers, vol. 71, no. 9, pp. 4247–4260, 2024

    work page 2024

  9. [9]

    Real-time model predictive control of a dc-dc buck converter,

    K. Sawant, R. Caverly, J. Poon, and S. Dhople, “Real-time model predictive control of a dc-dc buck converter,” inIEEE Energy Conversion Congress and Exposition, 2024, pp. 3990–3996

    work page 2024

  10. [10]

    A fully analog implementation of model predictive control with appli- cation to buck converters,

    S. Pirrera, L. Calogero, F. Gabriele, D. Regruto, A. Rizzo, and G. Setti, “A fully analog implementation of model predictive control with appli- cation to buck converters,” 2025

    work page 2025

  11. [11]

    Model predictive control: MPC’s role in the evolution of power electronics,

    S. Kouro, M. A. Perez, J. Rodriguez, A. M. Llor, and H. A. Young, “Model predictive control: MPC’s role in the evolution of power electronics,”IEEE Ind. Electron. Mag., vol. 9, no. 4, pp. 8–21, 2015

    work page 2015

  12. [12]

    Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit,

    D. Tank and J. Hopfield, “Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit,” IEEE Trans. Circuits Syst., vol. 33, no. 5, pp. 533–541, 1986

    work page 1986

  13. [13]

    Unifying the Tank and Hopfield linear programming circuit and the canonical nonlinear programming circuit of Chua and Lin,

    M. Kennedy and L. Chua, “Unifying the Tank and Hopfield linear programming circuit and the canonical nonlinear programming circuit of Chua and Lin,”IEEE Trans. Circuits Syst., vol. 34, no. 2, pp. 210–214, 1987

    work page 1987

  14. [14]

    Neural networks for nonlinear programming,

    ——, “Neural networks for nonlinear programming,”IEEE Trans. Circuits Syst., vol. 35, no. 5, pp. 554–562, 1988

    work page 1988

  15. [15]

    Quadratic and linear optimization with analog circuits,

    S. Vichik, “Quadratic and linear optimization with analog circuits,” Ph.D. dissertation, Univ. of California, Berkeley, CA, USA, 2015

    work page 2015

  16. [16]

    Circuit implementation of proximal projection neural networks for composite optimization problems,

    J. Wu, X. He, Y . Niu, T. Huang, and J. Yu, “Circuit implementation of proximal projection neural networks for composite optimization problems,”IEEE Trans. Ind. Electron., vol. 71, no. 2, pp. 1948–1957, 2024

    work page 1948

  17. [17]

    Real- time solution strategy for linearly constrained quadratic programs with proportional-integral control and variants,

    K. Sawant, P. Seiler, M. R. Jovanovi ´c, J. Poon, and S. Dhople, “Real- time solution strategy for linearly constrained quadratic programs with proportional-integral control and variants,” inProc. Amer. Control Conf., 2025, pp. 910–917

    work page 2025

  18. [18]

    An equivalent circuit workflow for unconstrained optimization,

    A. Agarwal, C. Fiscko, S. Kar, L. Pileggi, and B. Sinopoli, “An equivalent circuit workflow for unconstrained optimization,” 2023

    work page 2023

  19. [19]

    An equivalent circuit approach to distributed optimization,

    A. Agarwal and L. Pileggi, “An equivalent circuit approach to distributed optimization,” 2023

    work page 2023

  20. [20]

    Optimization algorithm design via electric circuits,

    S. P. Boyd, T. Parshakova, E. K. Ryu, and J. J. Suh, “Optimization algorithm design via electric circuits,” inAdvances in Neural Informa- tion Processing Systems, A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, Eds., vol. 37. Curran Associates, Inc., 2024, pp. 68 013–68 081

    work page 2024

  21. [21]

    Solving linear and quadratic programs with an analog circuit,

    S. Vichik and F. Borrelli, “Solving linear and quadratic programs with an analog circuit,”Comput. Chem. Eng., vol. 70, pp. 160–171, 2014

    work page 2014

  22. [22]

    Analog circuit for real-time optimization of constrained control,

    R. M. Levenson and A. A. Adegbege, “Analog circuit for real-time optimization of constrained control,” inProc. Amer. Control Conf., 2016, pp. 6947–6952

    work page 2016

  23. [23]

    Analog solver for embedded model predictive control with application to quadruple tank system,

    J. N. Bruno, F. D. Moran, H. I. Khajanchi, and A. A. Adegbege, “Analog solver for embedded model predictive control with application to quadruple tank system,” inProc. Amer. Control Conf., 2021, pp. 4680– 4685

    work page 2021

  24. [24]

    Real-time selective harmonic minimization using a hybrid analog/digital computing method,

    J. Poon, M. Sinha, S. V . Dhople, and J. Rivas-Davila, “Real-time selective harmonic minimization using a hybrid analog/digital computing method,”IEEE Trans. Power Electron., vol. 37, no. 5, pp. 5078–5088, 2022

    work page 2022

  25. [25]

    A hybrid- computing solution to nonlinear optimization problems,

    K. Sawant, D. Nguyen, A. Liu, J. Poon, and S. Dhople, “A hybrid- computing solution to nonlinear optimization problems,”IEEE Trans. Circuits Syst. I Reg. Papers, pp. 1–14, 2024

    work page 2024

  26. [26]

    Rapid prototyping of constrained linear quadratic optimal control with field programmable analog array,

    T. Skibik and A. A. Adegbege, “Rapid prototyping of constrained linear quadratic optimal control with field programmable analog array,” in Proc. IEEE Conf. Decis. Control, 2018, pp. 1864–1869

    work page 2018

  27. [27]

    On the implementation of an interior- point filter line-search algorithm for large-scale nonlinear programming,

    A. W ¨achter and L. T. Biegler, “On the implementation of an interior- point filter line-search algorithm for large-scale nonlinear programming,” Mathematical Programming, vol. 106, no. 1, pp. 25–57, 2006

    work page 2006

  28. [28]

    Quasi-Lagrangian neural network for convex quadratic optimization,

    G. Costantini, R. Perfetti, and M. Todisco, “Quasi-Lagrangian neural network for convex quadratic optimization,”IEEE Transactions on Neural Networks, vol. 19, no. 10, pp. 1804–1809, 2008

    work page 2008

  29. [29]

    Nocedal and S

    J. Nocedal and S. J. Wright,Numerical Optimization, 2nd ed. New York: Springer, 2006

    work page 2006

  30. [30]

    New conditions for global stability of neural net- works with application to linear and quadratic programming problems,

    M. Forti and A. Tesi, “New conditions for global stability of neural net- works with application to linear and quadratic programming problems,” IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., vol. 42, no. 7, pp. 354–366, 1995

    work page 1995

  31. [31]

    Saddle-point convergence of con- strained primal-dual dynamics,

    A. A. Adegbege and M. Y . Kim, “Saddle-point convergence of con- strained primal-dual dynamics,”IEEE Control Systems Letters, vol. 5, no. 4, pp. 1357–1362, 2021

    work page 2021

  32. [32]

    A repository of convex quadratic program- ming problems,

    I. Maros and C. M ´esz´aros, “A repository of convex quadratic program- ming problems,”Optimization Methods and Software, vol. 11, no. 1-4, pp. 671–681, 1999

    work page 1999

  33. [33]

    AMPL benchmarking files,

    “AMPL benchmarking files,” http://bit.ly/4gQ3z7Z

    work page

  34. [34]

    AMPL nonlinear programming models and data files,

    “AMPL nonlinear programming models and data files,” https://plato.asu.edu/ftp/ampl-nlp-source/

    work page

  35. [35]

    IPOPT solver,

    “IPOPT solver,” https://coin-or.github.io/Ipopt/

    work page

  36. [36]

    AMPL library,

    “AMPL library,” https://amplpy.ampl.com/en/latest/

    work page