论文标题
自动修复凸优化问题
Automatic Repair of Convex Optimization Problems
论文作者
论文摘要
考虑到一个不可行的，无限的或病理凸优化的问题，一个自然的问题是：我们可以对问题的参数做出的最小变化是什么，以便该问题可以解决？在本文中，我们通过将其作为优化问题提出，涉及参数的凸正则化功能的最小化，但要受到参数导致可解决问题的限制。我们提出了一种启发式方法，用于近似于基于惩罚方法的近似问题，并且最近开发的方法可以有效地评估凸锥程序的求解的衍生物，相对于其参数。我们通过将其应用于最佳控制和经济学的示例来说明我们的方法。
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address this question by posing it as an optimization problem involving the minimization of a convex regularization function of the parameters, subject to the constraint that the parameters result in a solvable problem. We propose a heuristic for approximately solving this problem that is based on the penalty method and leverages recently developed methods that can efficiently evaluate the derivative of the solution of a convex cone program with respect to its parameters. We illustrate our method by applying it to examples in optimal control and economics.
