In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

The problem of a computationally feasible method of finding the discrete logarithm in a (large) finite field is discussed, presenting the main algorithms in this direction. Some cryptographic schemes based on the discrete logarithm are presented. Finally, the theory of linear recurring sequences is outlined, in relation to its applications in cryptology.

A polynomial complexity bound is established for an interior point path following algorithm for the monotone linear complementarity problem that is based on the Chen{Harker{Kanzow smoothing techniques. The fundamental diierence with the Chen{Harker and Kanzow algorithms is the introduction of a rescaled Newton direction. The rescaling requires the iterates to remain in the interior of the posit...

We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both theoretically and empirically, in spite of some preliminary work, effective generalizations of ADMM to multiple blocks is still unclear. In this paper, we propose a pa...

We propose a trust-region method for nonlinear semidefinite programs with box-constraints. The penalty barrier method can handle this problem, but the size of variable matrices available in practical time is restricted to be less than 500. We develop a trust-region method based on the approach of Coleman and Li (1996) that utilizes the distance to the boundary of the box-constraints into consid...

In this section we will give an (extremely) brief Introduction to the concept of interior point methods • Logarithmic Barrier Method • Method of Centers We have previously seen methods that follow a path On the boundary of the feasible region (Simplex). As the name suggest, interior point methods instead Follow a path through the interior of the feasible region.

The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, and Mizuno globally convergent infeasible interior point algorithm The inexact variation is shown to have the same convergence properties accepting a residual in both the primal and dual Newton step equation also ...

We study a method for parallel solution of elliptic partial di erential equations which decomposes the problem into a number of independent subproblems on subspaces of the underlying solution space. Using symmetries of the domain, we obtain up to 64 such subproblems for a 3 dimensional cube and the method reduces to a direct solver. In the general case, or when the subproblems are solved only a...

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...

and Applied Analysis 3 Additionally, we assume that there exist positive constants γ and γ such that 0 < γ ≤ 󵄩󵄩󵄩gk 󵄩󵄩󵄩 ≤ γ, ∀k ≥ 1, (21) then we have the following result. Theorem2. Consider the method (2), (8) and (12), where d k is a descent direction. If (21) holds, there exist positive constants ξ 1 , ξ 2 , and ξ 3 such that relations