Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs with general and nonnegative constraints. In each iteration, our approximately solves KKT system which avoids requirement that any primal or dual iterate is interior-point. The has so...

Symmetricity of an optimal solution of Semi-Definite Program (SDP) with certain symmetricity is discussed based on symmetry property of the central path that is traced by a primal-dual interior-point method. A symmetric SDP is defined by operators for rearranging elements of matrices and vectors, and the solution on the central path is proved to be symmetric. Therefore, it is theoretically guar...

We present new primal-dual algorithms for several network design problems. The problems considered are the generalized Steiner tree problem (GST), the directed Steiner tree problem (DST), and the set cover problem (SC) which is a subcase of DST. All our problems are NP-hard; so we are interested in approximation algorithms for them. First we give an algorithm for DST which is based on the tradi...

In the paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. The starting point is any positive primal-infeasible dual-feasible point in a large region. The method maintains positivity of the iterates which point satisfies primalinfeasible dual-feasible point. At each iterates it requires to solve approximately a nonlinear system. It is show...

This short communication analyses a boundedness property of the inverse of a Jacobian matrix that arises in regularized primal-dual interior-point methods for linear and nonlinear programming. This result should be a useful tool for the convergence analysis of these kinds of methods.

In this note we focus on a comparison of two eecient methods to solve quadratic constrained optimal control problems governed by elliptic partial-diierential equations. One of them is based on a generalized Moreau-Yosida formulation of the constrained optimal control problem which results in an active set strategy involving primal and dual variables. The second approach is based on interior poi...

This paper deals with a semidefinite program (SDP) having free variables, which often appears in practice. To apply the primal-dual interior-point method, we usually need to convert our SDP into the standard form having no free variables. One simple way of conversion is to represent each free variable as a difference of two nonnegative variables. But this conversion not only expands the size of...

Second-order cone programming (SOCP) is the problem of minimizing linear objective function over cross-section of second-order cones and an a ne space. Recently this problem gets more attention because of its various important applications including quadratically constrained convex quadratic programming. In this paper we deal with a primal-dual path-following algorithm for SOCP to show many of ...

In this paper we will deal with primal{dual interior point methods for solving the linear programming problem. We present a short step and a long step path{following primal{dual method and derive polynomial{ time bounds for both methods. The iteration bounds are as usual in the existing literature, namely O(pnL) iterations for the short step, and O(nL) for the long step variant. In the analysis...

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can ...