A sequential quadratically constrained quadratic programming method for unconstrained minimax problems

In this paper, a sequential quadratically constrained quadratic programming (SQCQP) method for unconstrained minimax problems is presented. At each iteration the SQCQP method solves a subproblem that involves convex quadratic inequality constraints and a convex quadratic objective function. The glob...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 362; no. 1; pp. 34 - 45
Main Authors: Jian, Jin-bao, Chao, Mian-tao
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.02.2010
Elsevier
Subjects:
Acceleration of convergence
Calculus of variations and optimal control
Convergence rate
Exact sciences and technology
Global convergence
Mathematical analysis
Mathematics
Minimax programs
Numerical analysis
Numerical analysis. Scientific computation
Quadratic constraints
Quadratic programming
Sciences and techniques of general use
Convergence rate
Minimax programs
Global convergence
Quadratic programming
Quadratic constraints
Strong convergence
Iteration
Mathematical analysis
Sequential method
Minimax problem
Inequality constraint
Convex function
Application
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:In this paper, a sequential quadratically constrained quadratic programming (SQCQP) method for unconstrained minimax problems is presented. At each iteration the SQCQP method solves a subproblem that involves convex quadratic inequality constraints and a convex quadratic objective function. The global convergence of the method is obtained under much weaker conditions without any constraint qualification. Under reasonable assumptions, we prove the strong convergence, superlinearly and quadratic convergence rate.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.08.046