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An Extended sequential quadratically constrained quadratic programming Algorithm for Nonlinear, Semidefinite, and Second-Order Cone programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2013年第2期156卷 183-212页

作者： Auslender, Alfred Univ Lyon 1 Inst Camille Jordan F-69365 Lyon France Ecole Polytech Dept Econ Palaiseau France

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.

关键词： sequential quadratic programming sequential quadratically constrained quadratic programming Nonlinear programming Semidefinite programming Second-order cone programming Global convergence

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A simply sequential quadratically constrained quadratic programming method of strongly sub-feasible directions for constrained optimization

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OPTIMIZATION 2013年第4期62卷 463-482页

作者： Jian, Jin-Bao Yang, Su-Min Tang, Chun-Ming Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China

This article presents a simply sequential quadratically constrained quadratic programming method of strongly sub-feasible directions for constrained optimization. The main direction is obtained by solving one subproblem which consists of a convex quadratic objective function, simply convex quadratic constraints. In order to avoid Maratos effect, correct the main search direction by a system of linear equations. In this work, we also present a new second-order approximate condition which is used to ensure that the unit step can be accepted. The global and superlinear convergence can be induced under some suitable conditions. In the end, we present a set of preliminary numerical experiments to illustrate the effectiveness of the method.

关键词： sequential quadratically constrained quadratic programming systems of linear equations strongly sub-feasible directions second-order approximate condition global convergence rate of convergence 90C30 49M37 65K05

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AN EXACT PENALTY METHOD FOR NONCONVEX PROBLEMS COVERING, IN PARTICULAR, NONLINEAR programming, SEMIDEFINITE programming, AND SECOND-ORDER CONE programming

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SIAM JOURNAL ON OPTIMIZATION 2015年第3期25卷 1732-1759页

作者： Auslender, Alfred Univ Lyon 1 Inst Camille Jordan F-69365 Lyon France

This paper presents an exact penalty method for solving optimization problems with very general constraints covering, in particular, nonlinear programming (NLP), semidefinite programming (SDP), and second-order cone programming (SOCP). The algorithm is called the sequential linear cone method (SLCM) because for SDP and SOCP the main cost of computation amounts to solving at each iteration a linear cone program for which efficient solvers are available. Restricted to NLP, SLCM is exactly a sequential quadratic program method. Under two basic conditions which concern only the data, it is proved that the sequence of iterates is bounded. Furthermore, in particular, when the feasible set is nonempty, under two additional constraint qualification conditions, it is proved that the cluster points are stationary points. In that case, it is established also that the sequence of penalty parameters eventually stays constant, and for a particular class of data it is proved that a unit step length can be obtained.

关键词： sequential quadratic programming sequential quadratically constrained quadratic programming nonlinear programming semidefinite programming second-order cone programming conic programming global convergence

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