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A Dynamic Penalty Parameter Updating Strategy for Matrix-Free Sequential Quadratic Optimization

James Burke(jvburke***at***uw.edu)
Frank Curtis(frank.e.curtis***at***gmail.com)
Hao Wang(wanghao1***at***shanghaitech.edu.cn)
Jiashan Wang(jsw1119***at***math.washington.edu)

Abstract: This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation of the search direction during each iteration, for which we consider the use of matrix-free methods. In particular, we develop a method that requires an inexact solve of a single QP subproblem to establish the convergence of the overall SQP method. It is known that SQP methods can be plagued by poor behavior of the global convergence mechanism. To confront this issue, we propose the use of an exact penalty function with a dynamic penalty parameter updating strategy to be employed within the subproblem solver in such a way that the resulting search direction predicts progress toward both feasibility and optimality. We present our parameter updating strategy and prove that, under reasonable assumptions, the strategy does not modify the penalty parameter unnecessarily. We also discuss a matrix-free subproblem solver in which our updating strategy can be incorporated. We close the paper with a discussion of the results of numerical experiments that illustrate the benefits of our proposed techniques.

Keywords: nonlinear optimization, sequential quadratic optimization, exact penalty functions, convex composite optimization, alternating direction methods, coordinate descent methods

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 03/25/2018
Entry Accepted: 03/25/2018
Entry Last Modified: 03/25/2018

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