A sequential quadratically constrained quadratic programming method for differentiable convex minimization

Masao Fukushima, Zhi Quan Luo, Paul Tseng

Research output: Contribution to journalArticle

36 Scopus citations

Abstract

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 ℓ1 exact penalty function as the line search merit function.

Original languageEnglish (US)
Pages (from-to)1098-1119
Number of pages22
JournalSIAM Journal on Optimization
Volume13
Issue number4
DOIs
StatePublished - Nov 20 2003

Keywords

  • Convex programming
  • Global convergence
  • Maratos effect
  • Quadratic convergence
  • Quadratically constrained quadratic programming

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