An Extended Sequential Quadratically Constrained Quadratic Programming Algorithm for Nonlinear, Semidefinite, and Second‐Order Cone Programming

An Extended Sequential Quadratically Constrained Quadratic Programming Algorithm for Nonlinear, Semidefinite, and Second‐Order Cone Programming

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Article ID: iaor20131978
Volume: 156
Issue: 2
Start Page Number: 183
End Page Number: 212
Publication Date: Feb 2013
Journal: Journal of Optimization Theory and Applications
Authors:
Keywords: programming: quadratic, programming: nonlinear, heuristics
Abstract:

This paper is concerned with nonlinear, semidefinite, and second‐order cone programs. A general algorithm, which includes sequential quadratic programming and sequential quadratically constrained quadratic programming methods, is presented for solving these problems. In the particular case of standard nonlinear programs, the algorithm can be interpreted as a prox‐regularization of the Solodov sequential quadratically constrained quadratic programming method presented in Mathematics of Operations Research (2004). For such type of methods, the main cost of computation amounts to solve a linear cone program for which efficient solvers are available. Usually, ‘global convergence results’ for these methods require, as for the Solodov method, the boundedness of the primal sequence generated by the algorithm. The other purpose of this paper is to establish global convergence results without boundedness assumptions on any of the iterative sequences built by the algorithm.

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