A new initialization or ‘Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path — our initial method (Algo...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗(κ) linear complementarity problems (LCPs). We generalize the analysis of BER’s primal-dual interior point algorithm for LP to P∗(κ) LCPs. New search directions and proximity measures are proposed based on a new kernel function which has linear growth term. We showed that if a strictly feasible starting point...

Many interior-point methods for linear programming are based on the properties of the logarithmic barrier function. After a preliminary discussion of the convergence of the (primal) projected Newton barrier method, three types of barrier method are analyzed. These methods may be categorized as primal, dual and primal-dual, and may be derived from the application of Newton’s method to different ...

In this paper the abstract of the thesis ”New Interior Point Algorithms in Linear Programming” is presented. The purpose of the thesis is to elaborate new interior point algorithms for solving linear optimization problems. The theoretical complexity of the new algorithms are calculated. We also prove that these algorithms are polynomial. The thesis is composed of seven chapters. In the first ch...

In this paper we develop several polynomial-time interior-point methods (IPM) for solving nonlinear primal-dual conic optimization problem. We assume that the barriers for the primal and the dual cone are not conjugate. This broken symmetry does not allow to apply the standard primal-dual IPM. However, we show that in this situation it is also possible to develop very efficient optimization met...

We generalize primal-dual interior-point methods for linear programming problems to the convex optimization problems in conic form. Previously, the most comprehensive theory of symmetric primal-dual interior-point algorithms was given by Nesterov and Todd 8, 9] for the feasible regions expressed as the intersection of a symmetric cone with an aane subspace. In our setting, we allow an arbitrary...

Abstract. This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L-setting is analyzed, but also a more involved L-analysis, q < ∞, is pr...