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

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 standa...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 156; H. 2; S. 183 - 212
1. Verfasser: Auslender, Alfred
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.02.2013
Springer Nature B.V
Springer Verlag
Schlagworte:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Convergence
Engineering
Invited Paper
Mathematics
Mathematics and Statistics
Methods
Nonlinearity
Operations Research/Decision Theory
Optimization
Optimization algorithms
Programming
Quadratic programming
Solvers
Studies
Theory of Computation
Semidefinite programming
Global convergence
Nonlinear programming
Sequential quadratic programming
Sequential quadratically constrained quadratic programming
Second-order cone programming
ISSN:0022-3239, 1573-2878
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Zusammenfassung: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0145-z