The authors studied in Preiß and Stoer (2003) the analyticity properties of infeasible-interior-point paths encountered in the context of semidefinite linear complementarity problems. It will be shown that these results allow for the design of infeasibleinterior-point methods of long-step type with an arbitrarily high order of local convergence for solving such problems.

Some Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the infeasible interiorpoint method for linear optimization of Roos [SIAM J. Optim., 16(4):1110–1136 (electronic), 2006] to symmetric optimization. This unifies the analysis for linear, second-order cone and semidefinite optimizations.

Linear complementarity problem noted (LCP) becames in present the subject of many reseach interest because it arises in many areas and it includes the two important domains in optimization:the linear programming (LP) and the convex quadratic (CQP) programming. So the researchers aims to extend the results obtained in (LP) and (CQP) to (LCP). Differents classes of methods are proposed to solve (...

Interior point methods proved to be efficient and robust tools for solving large–scale optimization problems. The standard infeasible–start implementations scope very well with wide variety of problem classes, their only serious drawback is that they detect primal or dual infeasibility by divergence and not by convergence. As an alternative, approaches based on skew–symmetric and self–dual refo...

We propose a family of directions that generalizes many directions proposed so far in interiorpoint methods for the SDP (semide nite programming) and for the monotone SDLCP (semide nite linear complementarity problem). We derive the family from the Helmberg-Rendl-Vanderbei-Wolkowicz/KojimaShindoh-Hara/Monteiro direction by relaxing its \centrality equation" into a \centrality inequality." Using...

A simple interior point method is proposed for solving a system of linear equations subject to nonnegativity constraints. The direction of update is de ned by projection of the current solution on a linear manifold de ned by the equations. Infeasibility is discussed and extension for free and bounded variables is presented. As an application, we consider linear programming problems and a compar...

Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al. [12] in linear programming, this paper gives an overview on results concerning ...

Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a ...

We present a generalization of a homogeneous self-dual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any \big-M" parameter or two-phase method, and it generates either a solution converging towards feasibility and complementarity simultaneously or a certiicate proving infeasibility. Moreover, if the MCP is polynomiall...