In this paper, we first present a brief infeasible interior-point method with full-Newton step for solving linear complementarity problem (LCP). The main iteration consists of a feasibility step and several centrality steps. First we present a full Newton step infeasible interior-point algorithm based on the classic logarithmical barrier function. After that a specific kernel function is introd...

Kojima, Shindoh and Hara proposed a family of search directions for the semidefinite linear complementarity problem (SDLCP) and established polynomial convergence of a feasible short-step pathfollowing algorithm based on a particular direction of their family. The question of whether polynomiality could be established for any direction of their family thus remained an open problem. This paper a...

In this paper, an interior-point algorithm  for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...

In this paper, we first present a brief review about the feasible interior-point algorithm for P∗(κ)-horizontal linear complementarity problems (HLCPs) based on new directions. Then we present a new infeasible interior-point algorithm for these problems. The algorithm uses two types of full-Newton steps which are called feasibility steps and centering steps. The algorithm starts from strictly f...

This chapter presents an algorithm that works simultaneously on primal and dual linear programming problems and generates a sequence of pairs of their interior feasible solutions. Along the sequence generated, the duality gap converges to zero at least linearly with a global convergence ratio (1 Yf/n); each iteration reduces the duality gap by at least Yf/n. Here n denotes the size of the probl...

A scheme|inspired from an old idea due to Mayne and Polak (Math. Prog., vol. 11, 1976, pp. 67{80)|is proposed for extending to general smooth constrained optimization problems a previously proposed feasible interior-point method for inequality constrained problems. It is shown that the primal-dual interior point framework allows for a signi cantly more e ective implementation of the Mayne-Polak...

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...

(4) Consider the point y = (1/2, 0, 0) ∈ Ω. Is y an interior point of Ω? Characterize all the feasible directions e = (e1, e2, e3) ∈ R at y (a picture could help). Is y a (strict) local maximizer of f? (5) Consider the point z = (1/2, 1/2, 1/2) ∈ Ω. Is z an interior point of Ω? Characterize all the feasible directions e = (e1, e2, e3) ∈ R at z. Is z a (strict) local maximizer of f? What is the ...