arXiv:2511.01813math.OCcs.CE2025-11被引 2

让复杂优化问题自动求解,新手也能快速试验。

Disciplined Biconvex Programming

  • 基于规则语法定义双凸问题,自动拆解为可解子问题
  • 无需手动设计算法,直接生成专用交替凸优化求解器
  • 适合机器学习、信号处理等领域研究者快速验证模型

我们提出受约束的双凸规划(DBCP),一种用于构建和求解双凸优化问题的建模框架。双凸优化广泛应用于机器学习、信号处理、计算科学和控制等领域。实际求解通常依赖于交替凸搜索(ACS)启发式方法,即交替固定一组变量优化另一组,使每次子问题变为凸问题并高效求解。然而,为特定双凸问题设计和实现ACS求解器需大量人力,易出错且耗时。DBCP将受约束凸规划的思想扩展至双凸问题,用户只需遵循少量语法规则即可自然表达问题。系统自动分解并转换为凸子问题,并生成定制化ACS求解器进行求解。该框架支持用户快速尝试不同双凸问题形式,无需凸优化专业知识。我们已将DBCP集成至开源Python库dbcp中,作为著名凸优化领域语言CVXPY的扩展。

原文摘要 · Abstract (English)

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.

双凸优化自动求解建模框架CVXPY

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