{"id":"c6fcee06-f524-4392-9d37-d6a69134af3f","arxiv_id":"2502.01055","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"CRISP is a primal-only sequential convex programming solver with a weighted l1 penalty merit function that solves contact-implicit motion planning problems from all-zero initialization.","lead":"This paper introduces CRISP, a sequential-convex solver for contact-implicit robot motion planning that works from all-zero or naive initial guesses on six benchmark tasks. It matters because robust planning through contact without hand-specified contact sequences could make online manipulation and locomotion more practical.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix A's proof of Theorem 8 analyzes a different subproblem (Eq. 19, full J(x) with linearized penalties) than the QP (Eq. 10) CRISP actually solves, and Assumption 7 does not make J quadratic; the stated convergence guarantee is therefore not established.","rationale":"The reader's weakest-assumption analysis already identifies the most load-bearing issue: the proof in Appendix A analyzes Eq. (19), which uses the full objective J(x), while the algorithm solves the trust-region QP model in Eq. (10). I agree this is the central theoretical flaw. The paper's stated convergence guarantee is a key contribution, and as written the proof does not establish it under Assumption 7 because Eq. (19) is not equivalent to Eq. (10) for general convex C^1 objectives. The reader's other concerns (Delta_min not guaranteed by Algorithm 1 and the likely epsilon_c typo in Table I) are real but secondary; the Delta_min issue is an assumption rather than a proof contradiction, and the epsilon_c typo does not affect the reported numerical results since the actual constraint violations are far below 1e-5. I also credit the paper's independent support: the open-source C++ implementation, the six benchmark problems, the real-world Push T experiment, and the reported 100% success rates on the first four tasks. Those empirical claims are not undermined by the proof gap and are consistent with the paper's practical significance. Therefore I do not recommend moving the verdict away from CONDITIONAL; the appropriate outcome is to require the authors to either restrict Theorem 8 to quadratic objectives (which covers their benchmarks) or supply a proof that analyzes the actual subproblem (10) under clarified smoothness assumptions.","tokens_in":25046,"tokens_out":12177,"duration_ms":136330,"concrete_test":"One check: instantiate the scalar problem J(x) = x^4/4 + x^2, equality constraint c(x) = x - 1, mu = 1, x_k = 0, Delta >= 1. Solve subproblem (10): min_p p^2 + |p - 1| gives p = 0.5. Solve Eq. (19): min_x x^4/4 + x^2 + |x - 1| gives x approximately 0.4534. These minimizers differ, proving Eq. (19) is not a rewrite of (10). Then independently re-derive Theorem 8's limit argument from the actual first-order condition of (10), 0 in grad J_k + Hessian J_k p_k + sum_i mu_i grad c_i partial |.|, letting p_k -> 0; if that derivation cannot be completed under Assumption 7, Theorem 8's current proof fails and needs the stated quadratic or C^2 repair.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical claim is Theorem 8: convergence to a stationary point of the merit function (8) under Assumption 7, provided iterates converge and the trust-region radius stays bounded below. The proof in Appendix A is the only support. Eq. (19) states x_{k+1} = argmin_x J(x) + sum_i mu_i |c_i(x_k) + grad c_i(x_k)^T (x - x_k)|. This is not the subproblem the algorithm solves. Algorithm 1 solves the trust-region QP (10), whose objective is a quadratic Taylor model of J (J_k + grad J_k^T p + 0.5 p^T Hessian J_k p) plus l1 penalties on linearized constraints, with slacks v, w, t and the trust-region constraint. For a general convex C^1 J, Eq. (19) is not a rewrite of (10); the proof's subsequent use of grad J(x_{n_k+1}) is valid only for the full-J subproblem, not for the QP's first-order condition. Assumption 7 only requires J convex and C^1, so the Hessian used in (10) need not even exist. Thus the proof does not connect the object analyzed with the object actually solved. The theorem may be salvageable under a quadratic-J assumption, or under C^2 plus bounded Hessian by proving directly with the QP's KKT conditions, but as written it is incomplete. The empirical section (100% success, released code, real-world MPC) is independent of this theoretical flaw and appears credible.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes CRISP, a primal-only sequential convex programming solver for contact-implicit motion planning. At each iteration CRISP solves a trust-region convex QP that linearizes constraints and uses a quadratic model of the objective, with a weighted l1 penalty merit function to balance objective reduction and constraint satisfaction. The authors claim sufficient conditions for convergence of CRISP iterates to stationary points of the merit function (Theorem 8), a local-optimality correspondence (Proposition 9), an open-source C++ implementation, and benchmarks on six contact-implicit tasks showing 100% success for CRISP on the first four tasks, including all-zero initializations, plus a real-world push experiment with a Franka robot. The central theoretical proof in Appendix A is the main point of concern: it analyzes a different subproblem than the QP actually solved by the algorithm.","tokens_in":25446,"tokens_out":3549,"duration_ms":39526,"significance":"If the convergence guarantee is properly established, the paper makes a valuable practical contribution: a primal-only method that avoids the constraint-qualification failures of MPCC and shows surprising robustness from naive or zero initializations. The empirical core is substantial and credible: six planning problems, comparisons against SNOPT, IPOPT, PROXNLP, LCQpow, and Gurobi, a real-world MPC validation, and a released C++ implementation with reproducible benchmarks. These strengths are independent of the theoretical gap, and the open-source artifacts materially increase the paper's value. The theoretical claim, however, is load-bearing for the paper's abstract and Section II, and the proof as written does not connect the analyzed object to the implemented algorithm.","major_comments":[{"comment":"The proof of Theorem 8 analyzes a subproblem that is not the one CRISP solves. Equation (19) defines x_{k+1} as the minimizer of J(x) plus l1 penalties on linearly approximated constraints, whereas Algorithm 1 solves the trust-region QP (10), whose objective is a quadratic Taylor model of J with a Hessian term and an explicit trust-region constraint. For a general convex C^1 objective, these two subproblems are not equivalent, and the proof's use of the first-order condition of the full-J subproblem, e.g. the appearance of grad J(x_{n_k+1}) in Eq. (24)-(26), is not justified for the QP. No argument is given that a solution of (10) is also a minimizer of (19), so the theorem's conclusion is not established for the actual algorithm.","section":"Appendix A, Eq. (19)"},{"comment":"The hypotheses of Theorem 8 do not match the algorithm's construction or termination criteria. Assumption 7 only requires J to be convex and continuously differentiable, but subproblem (10) uses the Hessian of J, which need not exist under this assumption. Additionally, Theorem 8 assumes the trust-region radius remains bounded below by some Delta_min > 0, yet Algorithm 1 declares convergence when Delta_{k+1} < epsilon_r (line 29) and contains no mechanism to enforce or verify a uniform lower bound. Thus the stated sufficient conditions are not verifiable from the algorithm's own data, contrary to the claim in Section II that the convergence conditions are numerically checkable. The theorem may be salvageable by assuming J is C^2 with bounded Hessian and by proving convergence directly from the KKT conditions of (10), or by adding a separate safeguard that prevents the trust region from shrinking below a positive threshold.","section":"Section II, Assumption 7 and Algorithm 1"},{"comment":"The theorem's conclusion is about stationarity of the merit function (8), and Proposition 9 then states that a feasible local minimizer of the merit function is a local minimizer of the original problem. However, the paper explicitly acknowledges in Remark 3 and in the limitations section that the relationship between merit-function stationary points and local solutions of the original MPCC is not fully understood. That acknowledgment is appropriate, but it means the convergence theorem alone does not provide a guarantee about the quality of the contact-implicit solution unless an additional verification step is performed, which the paper does not provide. The empirical results remain informative, but the theoretical framing should be adjusted to reflect this gap.","section":"Theorem 8 and Proposition 9"}],"minor_comments":[{"comment":"The value of epsilon_c is listed as 1e6, which conflicts with the success criterion of constraint violation below 1e-5 stated in Section IV-C. This appears to be a typo, likely epsilon_c = 1e-6, and should be corrected.","section":"Table I"},{"comment":"The sentence beginning 'It is noteworthy to point that' is incomplete and should be finished or removed.","section":"Section III, user interface paragraph"},{"comment":"The header and row for PROXNLP are malformed: 'PROXNLP60' appears to merge the solver name with its success rate, and the success rate for PROXNLP in the cartpole task is unclear. The table formatting should be fixed.","section":"Table II"},{"comment":"The explanation of the complementarity constraint says it should be interpreted as phi_i(x,lambda)*lambda_i = 0 or phi_i(x,lambda)*lambda_i <= 0 as suggested by [22]. The inequality form is not a standard complementarity condition; this phrasing should be clarified to avoid confusion.","section":"Eq. (6e) and surrounding text"},{"comment":"The convergence check uses an OR condition between Delta_{k+1} < epsilon_r and ||p_k||_infty < epsilon_p, but Theorem 8 assumes a uniform lower bound Delta_min > 0. The stopping criterion based on a shrinking trust region is not covered by the theorem and should be discussed explicitly.","section":"Algorithm 1, line 29"}],"recommendation":"major_revision","confidential_remarks":"The theoretical gap in Appendix A is real and load-bearing: the proof analyzes Eq. (19), not the QP in Eq. (10), and Assumption 7 does not supply the Hessian needed by the algorithm. However, the empirical contribution is strong and reproducible, and the theorem appears salvageable with a C^2 assumption and a direct QP-based proof. I therefore recommend major revision rather than rejection. The editor may also wish to check whether the paper's claim of being the first to prove convergence for a sequential convex programming method in this contact-implicit setting is appropriate given the existing SCP convergence literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the paper in one breath: CRISP is a sequential-convex solver for contact-implicit motion planning that refuses to use dual variables, solves a trust-region QP at each iteration, scores iterations with a weighted l1 merit function, and—the headline—reliably produces feasible, low-tracking-error trajectories from all-zero or naive initial guesses on six benchmark tasks. The benchmarks are solid: comparisons against SNOPT, IPOPT, PROXNLP, LCQpow, Gurobi (MIQCP), a real-world push task with a Franka arm, and open-sourced C++ code. I believe the 100% success rates on the first four tasks; the box plots show CRISP with tight distributions while others have long tails. If you do contact-rich planning, this is a solver worth trying.\n\nWhat's new: the primal-only formulation for contact-implicit MPCC, plus the particular combination of trust regions, elastic mode, second-order correction, and per-constraint penalty update. Each ingredient is known; the combination is new and the all-zero initialization result is a genuine practical advance.\n\nWhere it's soft: the convergence theorem, Theorem 8, is not proven for the algorithm actually implemented. The proof in Appendix A replaces the QP (10)—which uses a quadratic Taylor model of J plus slack variables and a trust region—with subproblem (19), which minimizes the true J(x) plus linearized penalties directly. Those are not the same problem for a general convex C^1 J, and Assumption 7 doesn't even require J to be twice differentiable, so the Hessian in (10) need not exist. The theorem may be salvageable under C^2 with bounded Hessian, or for quadratic J, but as written it is incomplete. There's also a mismatch between the theorem's assumption that the trust-region radius is bounded below by Delta_min and Algorithm 1, which stops when Delta drops below epsilon_r. That's less damning—the theorem is about a convergent sequence—but the paper's claim that the conditions are 'numerically verifiable' overstates things. Finally, Table I lists epsilon_c = 1e6, which is almost certainly a typo for 1e-6; as printed, the 'constraint violation' tolerance would make the success criterion trivial.\n\nNone of this undermines the empirical core. The failure of SNOPT/IPOPT/PROXNLP on these problems is consistent with known MPCC issues, and CRISP's robustness is displayed with enough detail to be believable. The proof should be fixed or explicitly weakened to a claim about the simplified model.\n\nWho's this for: anyone working on contact-implicit optimization, robot manipulation, or locomotion. It deserves a serious referee—the empirical contribution and released code warrant that. I'd send it out but with a clear request to fix the theory or downgrade the claim.","headline":"Credible empirical robustness from all-zero initialization, but the convergence proof analyzes a different subproblem than the algorithm solves; the theory needs repair before the guarantee is taken at face value.","tokens_in":25923,"tokens_out":3299,"would_cite":true,"duration_ms":34100,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90C33","90C55","90C30"],"pacs":[],"model":"deepseek-v4-flash","headline":"A primal-only convex solver plans through contact from scratch","keywords":["contact-implicit motion planning","mathematical program with complementarity constraints","sequential convex programming","trust-region method","l1 penalty merit function","primal-only optimization","trajectory optimization"],"falsifier":"Instrument the released implementation on the six benchmark tasks to log the trust-region radius and the merit function's directional derivative at termination; if any returned point has the radius below the stopping tolerance and a negative directional derivative in some direction, then the sufficient conditions of the main theorem are not satisfied.","tokens_in":24841,"feed_emoji":"🤖","tokens_out":6755,"duration_ms":69840,"temperature":0.7,"pith_summary":"This paper claims that contact-implicit motion planning, an optimization problem made notoriously hard by complementarity constraints that violate classical constraint qualifications, can be solved robustly by a primal-only sequential convex method. The proposed solver, CRISP, replaces the usual search for KKT primal-dual pairs with a sequence of convex trust-region quadratic programs, judging progress with a weighted $\\ell^1$ penalty merit function. The paper proves sufficient conditions under which the iterates converge to a stationary point of that merit function, and shows that a feasible local minimizer of the merit function is a local minimizer of the original problem. On six planning tasks, CRISP is reported to discover usable contact sequences from naive and even all-zero initial guesses while established nonlinear solvers often fail or stall. If the method holds, contact-rich manipulation and locomotion planning would no longer need hand-specified contact modes or costly relaxation schemes.","feed_headline":"Contact planning solved from scratch by a primal-only solver","feed_subtitle":"A trust-region convex method beats KKT-based solvers on six contact-rich tasks, even from zero.","key_machinery":"The load-bearing object is the weighted $\\ell^1$ merit function $\\varphi_1(x;\\mu) = J(x) + \\sum_{i\\in E} \\mu_i |c_i(x)| + \\sum_{i\\in I} \\mu_i [c_i(x)]^-$, with a separate penalty weight for each constraint. CRISP minimizes it by repeatedly solving the convex trust-region quadratic program: a quadratic model of the convex objective, first-order linearizations of the constraints, slack variables that absorb the $\\ell^1$ penalties, and an $\\ell_\\infty$ bound on the trial step. Each trial step is accepted or rejected according to the ratio of actual to predicted decrease in the merit function, and a second-order correction re-linearizes the constraints using the value already computed at the trial point, preserving the convex QP structure. The convergence proof works by passing to a subsequence on which the signs of the linearized constraint quantities are constant, then comparing directional derivatives of the subproblem model with those of the merit function.","core_discovery":"The central discovery is that when the objective is convex, as quadratic tracking costs typically are, a method that never maintains dual variables and only drives down a weighted $\\ell^1$ penalty merit function can still reach first-order stationary points. The main theorem states that if the sequence of convex trust-region subproblems converges to some point and the trust-region radius stays bounded below by a positive constant, then that limit is a stationary point of the merit function. The companion local-optimality result closes the loop: a feasible local minimizer of the merit function is a local minimizer of the original contact-implicit problem. The paper then demonstrates empirically that CRISP attains 100 percent success on the first four benchmark tasks and credible solutions on the hopper and waiter problems, all from naive or all-zero initializations, in contrast to the benchmarked primal-dual solvers.","pith_inferences":["If the robustness comes from convex objectives plus primal-only penalization, the same trust-region QP structure should transfer to other MPCC instances in robotics, such as legged locomotion with nonlinear friction cones, where the subproblem remains convex.","The paper leaves open whether the limit point of CRISP is feasible for the original problem; a testable extension is to add an outer feasibility-repair phase that projects the merit-function stationary point onto the nonlinear constraints and then restarts CRISP.","Because the subproblem uses the objective Hessian while Assumption 7 assumes only continuous differentiability, a more careful convergence proof could replace the Hessian with a bounded positive-definite approximation, aligning the certified regime with what the algorithm actually assumes.","The benchmarks count success by tracking error and constraint-violation thresholds; a natural further test is whether the discovered contact sequences remain valid under model mismatch, building on the real-world push experiments."],"forward_implications":["If CRISP converges to a feasible local minimizer of the merit function, that point is also a local minimizer of the original contact-implicit problem, by Proposition 9.","On the four benchmark tasks, CRISP reports 100 percent success from naive or all-zero initial guesses, with the lowest median tracking error and constraint violation among the compared solvers.","On the hopper and waiter tasks, CRISP produces substantially lower objective values than the interior-point baseline, and in real-world push experiments it replans within about 80 milliseconds per cycle.","The convergence conditions of the main theorem are numerically checkable, so individual runs can be certified as reaching a stationary point of the merit function.","A mixed-integer reformulation of the Push T task becomes intractable beyond roughly four planning steps, whereas CRISP solves the same task in contact-implicit form."],"supporting_citations":[{"why":"Introduces the contact-implicit trajectory-optimization formulation in which all benchmark problems are cast.","marker":"[47]"},{"why":"Establishes that mathematical programs with complementarity constraints fail the standard constraint qualifications, motivating the primal-only design.","marker":"[48]"},{"why":"Documents the infeasible-subproblem failure of SQP methods on MPECs, motivating the elastic, always-feasible subproblem construction.","marker":"[22]"},{"why":"Supplies the exact-penalty theory behind the weighted l1 merit function.","marker":"[19]"},{"why":"Provides the trust-region and penalty machinery used in the convergence proof and in the algorithm design.","marker":"[46]"},{"why":"The sparse sequential-quadratic-programming baseline solver compared against in the benchmarks.","marker":"[24]"},{"why":"The interior-point baseline solver compared against, especially on the hopper and waiter tasks.","marker":"[57]"},{"why":"The linear-complementarity QP baseline that CRISP outperforms on the transport and waiter tasks.","marker":"[28]"},{"why":"Source of the waiter task formulation used as a benchmark.","marker":"[60]"}],"fun_headline_variants":["Zero-init contact planning solved by primal-only convex solver","CRISP: convex trust-region method handles zero-start contact plans","Primal-only sequential convex programming robust in contact planning","Contact-implicit planning works even from all-zero initial guesses","New solver achieves contact plans from scratch via convex QPs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The theorem assumes the iterates converge while the trust-region radius stays bounded above zero, but Algorithm 1 stops when that radius falls below a tolerance and never verifies the assumed lower bound.","fun_headline_variants_meta":{"raw":{"variants":["Zero-init contact planning solved by primal-only convex solver","CRISP: convex trust-region method handles zero-start contact plans","Primal-only sequential convex programming robust in contact planning","Contact-implicit planning works even from all-zero initial guesses","New solver achieves contact plans from scratch via convex QPs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000229,"raw_usage":{"total_tokens":1456,"prompt_tokens":897,"completion_tokens":559,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":513,"completion_tokens_details":{"reasoning_tokens":478}},"tokens_in":513,"tokens_out":559,"duration_ms":5853,"temperature":1.0,"reasoning_tokens":478,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T16:45:01.692265+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Instrument the released implementation on the six benchmark tasks to log the trust-region radius and the merit function's directional derivative at termination; if any returned point has the radius below the stopping tolerance and a negative directional derivative in some direction, then the sufficient conditions of the main theorem are not satisfied.","supporting_citations":[{"cited_title":"A direct method for trajectory optimization of rigid bodies through contact","cited_arxiv_id":null,"evidence_quote":"Introduces the contact-implicit trajectory-optimization formulation in which all benchmark problems are cast."},{"cited_title":"Mathematical pro- grams with complementarity constraints: Stationarity, optimality, and sensitivity","cited_arxiv_id":null,"evidence_quote":"Establishes that mathematical programs with complementarity constraints fail the standard constraint qualifications, motivating the primal-only design."},{"cited_title":"Local convergence of sqp methods for math- ematical programs with equilibrium constraints","cited_arxiv_id":null,"evidence_quote":"Documents the infeasible-subproblem failure of SQP methods on MPECs, motivating the elastic, always-feasible subproblem construction."},{"cited_title":"Fletcher","cited_arxiv_id":null,"evidence_quote":"Supplies the exact-penalty theory behind the weighted l1 merit function."},{"cited_title":"Numerical opti- mization","cited_arxiv_id":null,"evidence_quote":"Provides the trust-region and penalty machinery used in the convergence proof and in the algorithm design."},{"cited_title":"Gill, Walter Murray, and Michael A","cited_arxiv_id":null,"evidence_quote":"The sparse sequential-quadratic-programming baseline solver compared against in the benchmarks."},{"cited_title":"On the imple- mentation of an interior-point filter line-search algorithm for large-scale nonlinear programming","cited_arxiv_id":null,"evidence_quote":"The interior-point baseline solver compared against, especially on the hopper and waiter tasks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The linear-complementarity QP baseline that CRISP outperforms on the transport and waiter tasks."}],"review_version":1}