Disciplined Bilevel Programming

2026-08-31

AI Summary

本文提出了一种符号框架DBLP，用于以高阶可读方式指定和解决双层优化问题，并通过自动正则化和连续逼近法求解。

Abstract

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.

Problem

• bilevel optimization
• hierarchical decision problems
• manual analysis and reformulation

Innovation

• Disciplined Bilevel Programming
• Canonicalization
• Conic Karush-Kuhn-Tucker Conditions
• Complementarity Constraint Relaxation
• Gap Continuation Procedure