A Sequential Quadratically Constrained Quadratic Programming Method for Differentiable Convex Minimization

This paper presents a sequential quadratically constrained quadratic programming (SQCQP) method for solving smooth convex programs. The SQCQP method solves at each iteration a subproblem that involves convex quadratic inequality constraints as well as a convex quadratic objective function. Such a qu...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on optimization Vol. 13; no. 4; pp. 1098 - 1119
Main Authors: Fukushima, Masao, Luo, Zhi-Quan, Tseng, Paul
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2003
Subjects:
Applied mathematics
Approximation
Lagrange multiplier
Methods
Quadratic programming
ISSN:1052-6234, 1095-7189
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper presents a sequential quadratically constrained quadratic programming (SQCQP) method for solving smooth convex programs. The SQCQP method solves at each iteration a subproblem that involves convex quadratic inequality constraints as well as a convex quadratic objective function. Such a quadratically constrained quadratic programming problem can be formulated as a second-order cone program, which can be solved efficiently by using interior point methods. We consider the following three fundamental issues on the SQCQP method: the feasibility of subproblems, the global convergence, and the quadratic rate of convergence. In particular, we show that the Maratos effect is avoided without any modification to the search direction, even though we use an ordinary $\ell_1$ exact penalty function as the line search merit function.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623401398120