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Automatic repair of convex optimization problems
Optimization and Engineering ( IF 2.1 ) Pub Date : 2020-05-23 , DOI: 10.1007/s11081-020-09508-9
Shane Barratt , Guillermo Angeris , Stephen Boyd

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.



中文翻译:

自动修复凸优化问题

给定一个不可行的,无界的或病理性的凸优化问题,一个自然要问的问题是:我们可以对问题的参数进行的最小更改是什么,以使问题可以解决?在本文中,我们将这个问题作为一个优化问题来解决,该问题涉及参数的凸正则化函数的最小化,但要以参数导致可解决问题为约束。我们提出了一种基于惩罚方法的启发式方法,用于近似解决该问题,并利用了最近开发的方法,该方法可以有效地评估凸锥程序的解关于其参数的导数。我们通过将其应用于最优控制和经济学示例中来说明我们的方法。

更新日期:2020-05-23
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