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A quadratically approximate framework for constrained optimization, global and local convergence

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Abstract

This paper presents a quadratically approximate algorithm framework (QAAF) for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification (MFCQ), and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification (CRCQ) as well as the strong second-order sufficiency conditions (SSOSC). As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, P. R. China

    Jin Bao Jian

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  1. Jin Bao Jian
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Correspondence to Jin Bao Jian.

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Projects supported by NSFC (Nos. 10261001, 10771040) and Guangxi Province Science Foundation (No. 0640001)

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Jian, J.B. A quadratically approximate framework for constrained optimization, global and local convergence. Acta. Math. Sin.-English Ser. 24, 771–788 (2008). https://doi.org/10.1007/s10114-007-4465-0

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  • DOI: https://doi.org/10.1007/s10114-007-4465-0

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