A new SQP algorithm and numerical experiments for nonlinear inequality constrained optimization problem
 Abstract
 Keywords
 References

Abstract
In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown.
Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.

References
 M. S. Bazaraa, C. M. Shetly, Nonlinear Programming Theory and Algorithms, AWiley, New York, 1979.
 J. Birge, L. Qi, Z. Wei, A variant of the TopkisVeinott method for solving inequality constrained optimization problems, J. Appl. Math. Optim. 41 (2000)309330.
 J. F. Bonnans, E. R. Panier, A. L. Tits, J. Zhou, Avoiding the Maratos effect by means of a nonmonotone line search II: Inequality constrained problemsfeasible iterate, SIAM J. Numer. Anal. 29 (1992) 11871202.
 X. B. Chen, M. M. Kostreva, A generalization of the normrelaxed method of feasible directions, Appl. Math. Comput.102 (1999) 257272.
 F. Facchinei, S. Lucidi, Quadratically and superlinearly convergent for the solution of inequality constrained optimization problem, JOTA 85 (1995) 265289.
 M. Fukushima, A successive quadratic programming algorithm with global and superlinear convergence properties, Math. Programming 35 (1986) 253264.
 S. P. Han, Superlinearly convergent variable metric algorithm for general nonlinear programming problems, Math. programming 11 (1976) 263282. W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, vol. 187, Springer, Berlin, 1981.
 M. M. Kostreva, X. Chen, A superlinearly convergent method of feasible directions, Appl. Math. Comput. 116 (2000) 245255.
 C. T. Lawrence, A. L. Tits, Nonlinear equality constraints in feasible sequential quadratic programming, Optim. Methods Softw. 6 (1996) 265282.
 C. T. Lawrence, A. L. Tits, A computationally efficient feasible sequential quadratic programming algorithm, SIAM J. Optim. 11 (2001) 10921118.
 N. Maratos, Exact penalty functions for finite dimensional and control optimization problems, Ph. D. Thesis, University of Science and Technology, London, 1978. D. Q. Mayne, E. Polak, A superlinearly convergent algorithm for constrained optimization problems, Math. Programming 16 (1982) 4561.
 E. R. Panier, A. L. Tits, A superlinearly convergent feasible method for the solution of inequality constrained optimization problems, SIAM J. Control Optim. 25 (1987) 934950.
 E. R. Panier, A. L. Tits, On combining feasibility, descent and superlinear convergence in inequality constrained optimization, Math. Programing 59 (1993) 261276. E. R. Panier, A. L. Tits, J. N. Herskovits, A QPfree global convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J. Control Optim. 26 (1988) 788811.
 O. Pironneau, E. Polak, On the rate of convergence of certain methods for centers, Math. Programming 2 (1972) 230257.
 M. J. D. Powell, Y. Yuan, A fast algorithm for nonlinearly constrained optimization calculations, in: G. A. Waston (Ed.), Numerical Analysis, Springer, Berlin, 1978.
 M. J. D. Poweell, Y. Yuan, A recursive programming algorithm that uses differentiable exact penalty function, Math.Programming 35 (1986) 265278.
 P. Spellucci, An SQP method for general nonlinear programs using only equality constrained subproblems, Math.Programming 82 (1998) 413448.
 D. M. Topkis, A. F. Veinott, On the convergence of some feasible direction algorithms for nonlinear programming, SIAM J. Control 5 (1967) 268279.
 G. Zoutendijk, Methods of Feasible Directions, Elsevier, Amsterdam, 1960.
 Z. B. Zhu, An efficient sequential quadratic programming algorithm for nonlinear programming, Journal of Computational and Applied Mathematics, 175 (2005) 447464.
 Z. Zhu, A sequential equality constrained quadratic programming algorithm for inequality constrained optimization, Journal of Computational and Applied Mathematics, 212 (2008) 112125.

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