http://deepblue.lib.umich.edu/bitstream/2027.42/3660/5/ban6932.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3660/4/ban6932.0001.001.tx

Birge, John R.

Qi, Liqun

Wei, Zengxin

Deep Blue Documents at the University of Michigan

A variant of the Topkis-Veinott method for solving inequality constrained optimization problems

. In this paper, we give a variant of the Topkis-Veinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semi-definite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm is shown to be globally convergent in the sense that every accumulation point of the sequence generated by the algorithm is a Fritz-John point of the problem. We introduce a Fritz-John (FJ) function, an FJ1 strong second-order sufficiency condition (FJ1-SSOSC) and an FJ2 strong second-order sufficiency condition (FJ2-SSOSC), and then show, without any constraint qualification (CQ), that (i) if an FJ point z satisfies the FJ1-SSOSC, then there exists a neighborhood N(z) of z such that for any FJ point  y 2 N(z) n fzg, f 0 (y) 6= f 0 (z), where f 0 is the objective function of the problem; (ii) if an FJ point z satisfies the FJ2-SSOSC, then z is a strict local minimum of the problem. The resu..

J.R. Birge

L. Qi

Z. Wei

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A Variant of the Topkis-Veinott Method for Solving Inequality Constrained Optimization Problems

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.4592

A variant of the Topkis-Veinott method for solving inequality constrained optimization problems

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