Learning based convex approximation for constrained parametric optimization

• URL: http://arxiv.org/abs/2505.04037v1
• Date: Wed, 07 May 2025 00:33:14 GMT
• Title: Learning based convex approximation for constrained parametric optimization
• Authors: Kang Liu, Wei Peng, Jianchen Hu,
• Abstract summary: We propose an input neural network (ICNN)-based self-supervised learning framework to solve constrained optimization problems.<n>We provide rigorous convergence analysis, showing that the framework converges to a Karush-Kuhn-Tucker (KKT) approximation point of the original problem.<n>Our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.
• Score: 11.379408842026981
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism, our framework ensures \emph{non-strict constraint feasibility}, \emph{better optimality gap}, and \emph{best convergence rate} with respect to the state-of-the-art learning-based methods. We provide a rigorous convergence analysis, showing that the algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the original problem even when the internal solver is a neural network, and the approximation error is bounded. We test our approach on a range of benchmark tasks including quadratic programming (QP), nonconvex programming, and large-scale AC optimal power flow problems. The results demonstrate that compared to existing solvers (e.g., \texttt{OSQP}, \texttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.

Related papers

• Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms [1.4747234049753448]
  In high-stakes engineering applications, optimization algorithms must come with provable provablecase guarantees over a mathematically defined class of problems.<n>We describe the class of algorithms that achieve linear convergence for classes of nonsmooth composite optimization problems.
  arXiv  Detail & Related papers  (2025-08-01T16:56:42Z)
• Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints [49.76332265680669]
  This paper examines a crucial subset of problems where both the objective and constraint functions are weakly convex.<n>Existing methods often face limitations, including slow convergence rates or reliance on double-loop designs.<n>We introduce a novel single-loop penalty-based algorithm to overcome these challenges.
  arXiv  Detail & Related papers  (2025-04-21T17:15:48Z)
• Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimization [15.102119312523696]
  Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing.<n>We propose a learning-based approach that enhances existing non-learned approximation algorithms for CO.<n>Our method is trained end-to-end in a self-supervised fashion, using a novel gradient estimation scheme that treats the approximation algorithm as a black box.
  arXiv  Detail & Related papers  (2025-02-26T18:23:07Z)
• Scalable First-order Method for Certifying Optimal k-Sparse GLMs [9.613635592922174]
  We propose a first-order proximal gradient algorithm to solve the perspective relaxation of the problem within a BnB framework.<n>We show that our approach significantly accelerates dual bound computations and is highly effective in providing optimality certificates for large-scale problems.
  arXiv  Detail & Related papers  (2025-02-13T17:14:18Z)
• Learning to optimize with convergence guarantees using nonlinear system theory [0.4143603294943439]
  We propose an unconstrained parametrization of algorithms for smooth objective functions. Notably, our framework is directly compatible with automatic differentiation tools.
  arXiv  Detail & Related papers  (2024-03-14T13:40:26Z)
• GloptiNets: Scalable Non-Convex Optimization with Certificates [61.50835040805378]
  We present a novel approach to non-cube optimization with certificates, which handles smooth functions on the hypercube or on the torus. By exploiting the regularity of the target function intrinsic in the decay of its spectrum, we allow at the same time to obtain precise certificates and leverage the advanced and powerful neural networks.
  arXiv  Detail & Related papers  (2023-06-26T09:42:59Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching [55.28394191394675]
  We develop an adaptive inexact Newton method for equality-constrained nonlinear, nonIBS optimization problems. We demonstrate the superior performance of our method on benchmark nonlinear problems, constrained logistic regression with data from LVM, and a PDE-constrained problem.
  arXiv  Detail & Related papers  (2023-05-28T06:33:37Z)
• Can Decentralized Stochastic Minimax Optimization Algorithms Converge Linearly for Finite-Sum Nonconvex-Nonconcave Problems? [56.62372517641597]
  Decentralized minimax optimization has been actively studied in the past few years due to its application in a wide range machine learning. This paper develops two novel decentralized minimax optimization algorithms for the non-strongly-nonconcave problem.
  arXiv  Detail & Related papers  (2023-04-24T02:19:39Z)
• Learning to Optimize with Stochastic Dominance Constraints [103.26714928625582]
  In this paper, we develop a simple yet efficient approach for the problem of comparing uncertain quantities. We recast inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
  arXiv  Detail & Related papers  (2022-11-14T21:54:31Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming [17.9230793188835]
  We study nonlinear optimization problems with objective and deterministic equality and inequality constraints. We propose an active-set sequentialAdaptive programming algorithm, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the parameters of augmented Lagrangian and performs line search to decide the stepsize.
  arXiv  Detail & Related papers  (2021-09-23T17:12:17Z)
• A Feasible Level Proximal Point Method for Nonconvex Sparse Constrained Optimization [25.73397307080647]
  We present a new model of a general convex or non objective machine machine objectives. We propose an algorithm that solves a constraint with gradually relaxed point levels of each subproblem. We demonstrate the effectiveness of our new numerical scale problems.
  arXiv  Detail & Related papers  (2020-10-23T05:24:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.