A SUPERLINEAR CONVERGENCE MODIFIED FSQP METHOD FOR LINEAR CONSTRAINED OPTIMIZATION PROBLEMS
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Abstract
In this paper, a modified feasible sequential quadratic programming (FSQP) method is presented to solve the linear programming. By solving only one QP subproblem, a feasible descent direction is obtained. A high-order revised direction is computed by solving a linear system to avoid Maratos effect. Under some suitable conditions, the global and superlinear convergence can be obtained.
Keywords: FSQP method; Llinear constrained optimization; Global convergence; superlinear convergence rate
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G.Zoutendijk,Methods of Feasible Directions,Elsevier,Amsterdam,1960.
D.M.Topkis,A.F.Veinott.On the convergence of some feasible direction algorithms for nonlionear programming,SIAM J.Control 5(1967)268-279.
O.Pironneau,E.Polak,On the rate of convergence of certain method of centers,Math,Programming 2(1972)230-257.
S.P.Han,Superlinearly convergent variable metric algorithm for general nonlinear programming problems,Math Programming 11(1976) 263-282.
M.J.D.Powell,A fast algorithm for nonlinear constrained optimization calculations,in:G.A.Waston(Ed),Numerical Analysis,Springer,Berlin,1978,pp.144-157.
E.R.Panier,A.L.Tits,A Superlinearly convergent feasible method for the solution of inequality contrained optimization problems SIAM J.Control Optim.25(1987)934-950.
M.Fukushima. A successive quadratic programming algorithm with globle and superlinear convergence properties, Math.Programming 35(1986) 253-264.
E.R.Panier,A.L.Tits,On combining feasibility ,descent and Superlinearly convergence in inequality contrained optimization, Math.Programming 59(1993)261-276.
J. B. Jian. A Superlinearly and Quadraticly Convergent SQP Type Feasible Method for Constrained Optimization, Applied Mathematics A Journal of Chinese Universities (B), 15 :3 (2000), 319—332.
Z.B. Zhu,An efficient sequential quadratic programming algorithm for nonlinear programming,Journal of Computational and Applied Mathematics 175(2005)447-464
Z.B. Zhu,W.D. Zhang, Z.J. Geng. A feasible SQP method for nonlinear programming. Applied Mathematics and Computation, 2010, 215(11), 3956–3969.
Z.J Luo Z.B Zhu and G.H Chen. Modifying Feasible SQP Method for Inequality Constrained Optimization, Information Computing and Applications(Lecture Notes in Computer Science), 2012, 7473, 323-330.
Z.B. Zhu, A simple feasible SQP algorithm for inequality constrained optimization. Applied Mathematics and Computation, 2006, 182, 987-998.
N.Maratos, Exact penalty functions for finite dimensional and control optimization problems, Ph.D. Thesis, University of Science and Technology, London, 1978.