In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

We present an overview of available software for solving linear programming problems using interior-point methods. Some of the codes discussed include primal and dual simplex solvers as well, but we focus the discussion on the implementation of the interior-point solver. For each solver, we present types of problems solved, available distribution modes, input formats and modeling languages, as ...

In this paper we present a redesign of a linear algebra kernel of an interior point method to avoid the explicit use of problem matrices. The only access to the original problem data needed are the matrix-vector multiplications with the Hessian and Jacobian matrices. Such a redesign requires the use of suitably preconditioned iterative methods and imposes restrictions on the way the preconditio...

where x is an n-dimensional column vector of variables; A is an m×n matrix [aij ] with m rows of transposed n-dimensional column vectors ai , ∀i = 1, . . . ,m; b is an m-dimensional column vector; c is an n-dimensional column vector; and 0 is a column vector of zeros of appropriate dimension according to context. Simplex pivoting algorithms and polynomial interior-point barrier-function methods...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...

We introduce a class of algorithms for the solution of linear programs. This class is motivated by some recent methods suggested for the solution of complementarity problems. It reformulates the optimality conditions of a linear program as a nonlinear system of equations and applies a Newton-type method to this system of equations. We investigate the global and local convergence properties and ...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...

3. page 13, lines 12–13: Insert a phrase to stress that we consider only monotone LCP in this book, though the qualifier ”monotone” is often omitted. Replace the sentence preceding the formula (1.21) by The monotone LCP—the qualifier ”monotone” is implicit throughout this book—is the problem of finding vectors x and s in I R that satisfy the following conditions: 4. page 13, line −12: delete “o...

We perform a smoothed analysis of Renegar’s condition number for linear programming by analyzing the distribution of the distance to ill-posedness of a linear program subject to a slight Gaussian perturbation. In particular, we show that for every n-by-d matrix Ā, n-vector b̄, and d-vector c̄ satisfying ∥∥Ā, b̄, c̄∥∥ F ≤ 1 and every σ ≤ 1, E A,b,c [logC(A, b, c)] = O(log(nd/σ)), where A, b and c ar...