Disciplined Biconvex Programming

• URL: http://arxiv.org/abs/2511.01813v2
• Date: Mon, 10 Nov 2025 13:20:19 GMT
• Title: Disciplined Biconvex Programming
• Abstract summary: We introduce disciplined bi programming (DBCP) for specifying solving bi computational processing problems.<n>Bi optimization problems arise in various applications, including machine learning signal, and science, and control.
• Score: 9.272977870242562
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce disciplined biconvex programming (DBCP), a modeling framework for specifying and solving biconvex optimization problems. Biconvex optimization problems arise in various applications, including machine learning, signal processing, computational science, and control. Solving a biconvex optimization problem in practice usually resolves to heuristic methods based on alternate convex search (ACS), which iteratively optimizes over one block of variables while keeping the other fixed, so that the resulting subproblems are convex and can be efficiently solved. However, designing and implementing an ACS solver for a specific biconvex optimization problem usually requires significant effort from the user, which can be tedious and error-prone. DBCP extends the principles of disciplined convex programming to biconvex problems, allowing users to specify biconvex optimization problems in a natural way based on a small number of syntax rules. The resulting problem can then be automatically split and transformed into convex subproblems, for which a customized ACS solver is then generated and applied. DBCP allows users to quickly experiment with different biconvex problem formulations, without expertise in convex optimization. We implement DBCP into the open source Python package dbcp, as an extension to the famous domain specific language CVXPY for convex optimization.

Related papers

• Disciplined Bilevel Programming [9.272977870242562]
  Bilevel optimization provides a natural modeling language for hierarchical decision problems.<n>Applying existing numerical solvers usually requires substantial manual analysis and reformulation.<n>We introduce disciplined bilevel programming (DBLP), a symbolic framework that allows users to specify and solve optimistic bilevel problems.
  arXiv  Detail & Related papers  (2026-09-01T03:22:48Z)
• An Expansion-Based Approach for Quantified Integer Programming [0.0]
  Quantified Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF)<n>QIP provides a versatile framework for addressing complex decision-making scenarios.<n>We introduce an expansion-based approach for QIP using Counterexample-Guided Abstraction Refinement (CEGAR)
  arXiv  Detail & Related papers  (2025-06-04T21:14:14Z)
• Efficient QAOA Architecture for Solving Multi-Constrained Optimization Problems [3.757262277494307]
  This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz.<n>One-hot constraints are enforced through $XY$-mixers that restrict the search space to the feasible sub-space naturally.<n>Since $XY$-mixers restrict the search space, specific state vector entries are always zero and can be omitted from the simulation, saving valuable memory and computing resources.
  arXiv  Detail & Related papers  (2025-06-03T17:46:53Z)
• Solving Inverse Problem for Multi-armed Bandits via Convex Optimization [10.218348617571257]
  We consider the inverse problem of multi-armed bandits (IMAB) that are widely used in neuroscience and psychology research for behavior modelling.<n>We first show that the IMAB problem is not convex in general, but can be relaxed to a convex problem via variable transformation.<n>We discuss a condition where our method provides global solution to the IMAB problem with certificate, as well as approximations to further save computing time.
  arXiv  Detail & Related papers  (2025-01-31T08:08:32Z)
• Differentiation Through Black-Box Quadratic Programming Solvers [21.717766458737426]
  Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP)<n>We introduce dQP, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver.<n>Building on this result, we provide a minimal-overhead, open-source implementation that seamlessly integrates with over 15 state-of-the-art solvers.
  arXiv  Detail & Related papers  (2024-10-08T20:01:39Z)
• A Near-Optimal Single-Loop Stochastic Algorithm for Convex Finite-Sum Coupled Compositional Optimization [53.14532968909759]
  We introduce an efficient single-loop primal-dual block-coordinate algorithm called ALEXR.<n>We establish the convergence rates of ALEXR in both convex and strongly convex cases under smoothness and non-smoothness conditions.<n> Experimental results on GDRO and partial Area Under the ROC Curve for cFCCO demonstrate the promising performance of our algorithm.
  arXiv  Detail & Related papers  (2023-12-04T19:00:07Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Numerical Methods for Convex Multistage Stochastic Optimization [86.45244607927732]
  We focus on optimisation programming (SP), Optimal Control (SOC) and Decision Processes (MDP) Recent progress in solving convex multistage Markov problems is based on cutting planes approximations of the cost-to-go functions of dynamic programming equations. Cutting plane type methods can handle multistage problems with a large number of stages, but a relatively smaller number of state (decision) variables.
  arXiv  Detail & Related papers  (2023-03-28T01:30:40Z)
• Functional Constrained Optimization for Risk Aversion and Sparsity Control [7.561780884831967]
  Risk and sparsity requirements need to be enforced simultaneously in many applications, e.g., in portfolio optimization, assortment planning, and radiation planning. We propose a Level Conditional Gradient (LCG) method, which generates a convex or sparse trajectory for these challenges. We show that the method achieves a level single-set projection of the optimal value an inner conditional approximation (CGO) for solving mini-max sub gradient.
  arXiv  Detail & Related papers  (2022-10-11T02:51:51Z)
• A Constrained Optimization Approach to Bilevel Optimization with Multiple Inner Minima [49.320758794766185]
  We propose a new approach, which convert the bilevel problem to an equivalent constrained optimization, and then the primal-dual algorithm can be used to solve the problem. Such an approach enjoys a few advantages including (a) addresses the multiple inner minima challenge; (b) fully first-order efficiency without Jacobian computations.
  arXiv  Detail & Related papers  (2022-03-01T18:20:01Z)
• Enhanced Bilevel Optimization via Bregman Distance [104.96004056928474]
  We propose a bilevel optimization method based on Bregman Bregman functions. We also propose an accelerated version of SBiO-BreD method (ASBiO-BreD) by using the variance-reduced technique.
  arXiv  Detail & Related papers  (2021-07-26T16:18:43Z)
• Recent Theoretical Advances in Non-Convex Optimization [56.88981258425256]
  Motivated by recent increased interest in analysis of optimization algorithms for non- optimization in deep networks and other problems in data, we give an overview of recent results of theoretical optimization algorithms for non- optimization.
  arXiv  Detail & Related papers  (2020-12-11T08:28:51Z)
• Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization [5.669790037378094]
  The goal is to find an optimal solution among a finite set of possibilities. Deep reinforcement learning (DRL) has shown its promise for solving NP-hard optimization problems. constraint programming (CP) is a generic tool to solve optimization problems. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving optimization problems.
  arXiv  Detail & Related papers  (2020-06-02T13:54:27Z)

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.