The paper introduces AutoConvexRelax, a learning-based framework that automates the design of convex relaxations for nonconvex optimization problems. By representing a problem as a tripartite graph of variables, symbolic terms, and objective/constraint positions, the method learns a policy to compose symbolic rewrites that generate valid relaxation trajectories. Experiments on quadratic and fractional problems show that the learned policy improves McCormick lower bounds by 13.52% and achieves near‑semidefinite bounds while using smaller formulations.
By Jinrun Liu, Bai Yan, Tengfei Liu, Qunfeng Liu, Jian Yang, Shi Cheng, Yuhui Shi, Qi Zhao
arXiv:2511.02821v2 Announce Type: replace-cross
Abstract: We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex s...
By Dan Garber
Second-order cone programs (SOCPs) are a fundamental class of convex optimization problems widely applied across engineering domains. Classical interior-point methods are robust and accurate, but thei...
arXiv:2606. 13825v1 Announce Type: cross Abstract: Deep unfolding (DU) accelerates iterative optimizers by introducing learnable components and training them through unrolled iterations, but extending DU to the large-scale semidefinite programs (SDPs) common in robotics has remained limited.
By Alex Oshin, Rahul Vodeb Ghosh, Evangelos A. Theodorou
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
By Andrea Martin, Ian R. Manchester, Luca Furieri
arXiv:2607. 20769v1 Announce Type: new Abstract: Learning-enabled decision systems often use offline data or computation to reduce online compute cost.
By Shijie Pan, Agustin Castellano, Zeyu Shen, Enrique Mallada
arXiv:2609. 30501v1 Announce Type: new Abstract: Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.
By Zhiyao Zhang, Menglu Yu, Alvaro Velasquez, Nathaniel D. Bastian, Jia Liu
arXiv:2409. 08066v3 Announce Type: replace Abstract: The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control.
By Lukas L\"uken, Sergio Lucia
arXiv:2607. 22467v1 Announce Type: new Abstract: Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve.
By Anjian Li, Ryne Beeson
The paper introduces Curvature-Scaled Sharpness-Aware Minimization (CS‑SAM), a variant of SAM that scales both the perturbation and descent step by curvature bounds to uniformly control gradient distortion under generalized smoothness conditions. It proves deterministic ≥1/T convergence rates for nonconvex objectives, last‑iterate ≥1/T rates for convex objectives, and linear convergence under the Polyak‑Łojasiewicz condition, while recovering standard gradient descent rates when the perturbation is zero. Experiments on computer vision tasks show that CS‑SAM, particularly the (H0,H1) variant, achieves the highest mean best‑test accuracy across four settings compared to tuned SAM and USAM.
By Dimitris Oikonomou, Nicolas Loizou
The paper introduces Convex-Concave Reinforcement Learning (CCRL), showing that the exact per‑iteration objective in policy learning can be expressed as a difference‑of‑convex (DC) program in log‑density‑ratio coordinates. This formulation unifies existing methods such as CPI, NPG, TRPO, and AWR as special cases and enables a multi‑step axis that couples consecutive decisions. Using sequential convex programming, the authors provide convergence guarantees and demonstrate that CCRL outperforms or matches PPO on diagnostic MDPs, classic control tasks, and a stochastic mid‑horizon healthcare domain, achieving faster convergence and higher training‑curve area.
By Shripad V. Deshmukh, Yaswanth Chittepu, Dhawal Gupta, Philip Thomas, Scott Niekum
HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
By Trinh Tran, Binh Nguyen, Truong X. Nghiem