发表机构
IMBIT; BrainLinks-BrainTools; Department of Computer Science, University of Freiburg（IMBIT; BrainLinks-BrainTools; 弗莱堡大学计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出约束双层规划（DBLP）框架，在CVXPY扩展包BLVPY中实现，可让用户用少量代码指定求解乐观双层优化问题，无需相关先验专业知识。
AI 中文摘要
双层优化为分层决策问题提供了自然的建模语言，但应用现有数值求解器通常需要大量手动分析和重构。本文介绍了约束双层规划（DBLP），这是一个符号框架，允许用户以接近数学公式的高级、人类可读的方式指定和求解乐观双层问题。对于上层为约束非线性问题、下层为满足约束参数化规划规则的凸问题，DBLP会自动将下层问题规范化为锥形式，并利用锥型Karush-Kuhn-Tucker条件构建等价的单层重构。我们对得到的互补性约束进行松弛，采用间隙延续过程近似求解一系列光滑非线性问题。我们在开源Python包BLVPY中实现了DBLP，BLVPY是CVXPY针对双层规划的扩展。我们在多个应用领域的一系列双层优化问题上展示了BLVPY的建模和求解能力。该框架及其实现使用户能在几行代码内指定和求解双层优化问题，无需具备双层建模和数值优化的先验专业知识。
英文摘要
Bilevel optimization provides a natural modeling language for hierarchical decision problems. However, applying existing numerical solvers usually requires substantial manual analysis and reformulation. In this paper, we introduce disciplined bilevel programming (DBLP), a symbolic framework that allows users to specify and solve optimistic bilevel problems in a high-level, human-readable way that is close to the mathematical formulation. For problems with a disciplined nonlinear upper problem and a convex lower problem satisfying the disciplined parameterized programming rules, DBLP automatically canonicalizes the lower problem into conic form and constructs an equivalent single-level reformulation using the conic Karush-Kuhn-Tucker conditions. We relax the resulting complementarity constraint and use a gap continuation procedure to approximately solve a sequence of smooth nonlinear problems. We implement DBLP in the open-source Python package BLVPY, an extension of CVXPY for bilevel programming. We demonstrate the modeling and solution capabilities of BLVPY on a range of bilevel optimization problems from several application domains. The proposed framework and implementation allow users to specify and solve bilevel optimization problems within a few lines of code, without prior expertise in bilevel modeling and numerical optimization.
