A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constrai...

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Bibliographic Details
Published inMathematical programming Vol. 92; no. 3; pp. 393 - 424
Main Authors Armand, Paul, Gilbert, Jean Charles, Jan, Sophie
Format Journal Article
LanguageEnglish
Published Springer Verlag 2002
Subjects
Mathematics
Optimization and Control
CONVEX PROGRAMMING
SHIFT AND SLACK VARIABLES
INFEASIBLE ITERATES
SUPERLINEAR CONVERGENCE
LINE-SEARCH
CONSTRAINED OPTIMIZATION
PRIMAL-DUAL METHOD
ANALYTIC CENTER
INTERIOR POINT ALGORITHM
BFGS QUASI-NEWTON APPROXIMATIONS
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ISSN0025-5610
1436-4646
DOI10.1007/s101070100283

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Summary:This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of the iterates is progressively enforced thanks to shift variables and an exact penalty approach. Global and $q$-superlinear convergenc- e is obtained for a fixed penalty parameter; global convergence to the analytic center of the optimal set is ensured when the barrier parameter tends to zero, provided strict complementarity holds.
ISSN:0025-5610
1436-4646
DOI:10.1007/s101070100283