A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...

This paper proposes a primal-dual interior-point filter method for nonlinear semidefinite programming, which is the first multidimensional (three-dimensional) filter methods for interior-point methods, and of course for constrained optimization. A freshly new definition of filter entries is proposed, which is greatly different from those in all the current filter methods. A mixed norm is used t...

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...

Sufficient conditions are given for the Q-superlinear convergence of the iterates produced by primal-dual interior-point methods for linear complementarity problems. It is shown that those conditions are satisfied by several well known interior-point methods. In particular it is shown that the iteration sequences produced by the simplified predictor–corrector method of Gonzaga and Tapia, the si...

Linear programming (LP) is an important field of optimization. Even though, interior point methods are polynomial algorithms, many LP practical problems are solved more efficiently by the primal and dual revised simplex methods (RSM); however, RSM has a poor performance in hard LP problems (HLPP) as in the Klee-Minty Cubes problem. Among LP methods, the hybrid method known as Simplex-Genetic (S...

The notion of weighted centers is essential in V-space interior-point algorithms for linear programming. Although there were some successes in generalizing this notion to semidefinite programming via weighted center equations, we still do not have a generalization that preserves two important properties — 1) each choice of weights uniquely determines a pair of primal-dual weighted centers, and ...

We discuss a possibility of the extension of a primal-dual interior-point algorithm suggested recently in 1]. We consider optimization problems deened on the intersection of a symmetric cone and an aane subspace. The question of solvability of a linear system arising in the implementation of the primal-dual algorithm is analyzed. A nondegeneracy theory for the considered class of problems is de...

Here we present an implementation of Primal-Dual Affine scaling method to solve linear optimisation problem on GPU based systems. Strategies to convert the system generated by complementary slackness theorem into a symmetric system are given. A new CUDA friendly technique to solve the resulting symmetric positive definite subsystem is also developed. Various strategies to reduce the memory tran...