Interior point method

May 14th, 2015
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Abstract. Interior-point methods require strictly feasible points as starting points. In theory, this requirement does not seem to be particularly restrictive, but it can be costly in computation. To overcome this deficiency, most existing practical algorithms allow positive but infeasible starting points and seek feasibility and optimality simultaneously.

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Interior point method ()SIAM J. OPTIMIZATIONDownloaded 02/21/14 to 128.42.163.118. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.phpVol. 4, No. 1, pp. 208-227, February 19941994 Society for Industrial and Applied Mathematics012ON THE CONVERGENCE OF A CLASS OF INFEASIBLEINTERIOR-POINT METHODS FOR THE HORIZONTAL LINEARCOMPLEMENTARITY PROBLEM*YINZHANGtAbstract. Interior-point methods require strictly feasible points as starting points. In theory, this requirement does not seem to be particularly restrictive, but it can be costly in computation. To overcome this deficiency, most existing practical algorithms allow positive but infeasible starting points and seek feasibility and optimality simultaneously. Algorithms of this type shall be called in]easible interior-point algorithms. Despite their superior performance, existing infeasible interiorpoint algorithms still lack a satisfactory demonstration of theoretical convergence and polynomial complexity. This paper studies a popular infeasible interior-point algorithmic framework that was implemented for linear programming in the highly successful interior-point code OB1 [I. J. Lustig, R. E. Marsten, and D. F. Shanno, Linear Algebra Appl., 152 (1991), pp. 191-222]. For generality, the analysis is carried out on a horizontal linear complementarity problem that includes linear and quadratic programming, as well as the standard linear complementarity problem. Under mi

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