In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...

ABSTRACT We describe efficient interior-point methods for the design of filters with constraints on the magnitude spectrum, for example, piecewise-constant upper and lower bounds, and arbitrary phase. Several researchers have observed that problems of this type can be solved via convex optimization and spectral factorization. The associated optimization problems are usually solved via linear pr...

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasibl...

We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is [_~-2 A v] instead of reducing to obtain the usual AD2A v system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the product AD2A v when A has dense columns; and (2) i...

In this paper we present the application of the interior-point decomposition (IPD) method, which was originally formulated for stochastic programming, to optimization problems involving multiple agents that are coupled through constraints and objectives. IPD eliminates the need to communicate local constraints and cost functions for all variables that relate to internal dynamics and objectives ...

We describe the analytic center cutting plane method and its relationship to classical methods of nondi erentiable optimization and column generation. Implementation issues are also discussed, and current applications listed. Keywords Projective Algorithm, Analytic Center, Cutting Plane Method. This work has been completed with support from the Fonds National Suisse de la Recherche Scienti que,...

The Kantorovich Theorem is a fundamental tool in nonlinear analysis which has been extensively used in classical numerical analysis. In this paper we show that it can also be used in analyzing interior point methods. We obtain optimal bounds for Newton’s method when relied upon in a path following algorithm for linear complementarity problems. Given a point z that approximates a point z(τ ) on ...

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

The starting point used by an interior point algorithm for linear and convex quadratic programming may significantly influence the behaviour of the method. A widely used heuristic to construct such a point consists of dropping variable nonnegativity constraints and computing a solution which minimizes the Euclidean norm of the primal (or dual) point while satisfying the appropriate primal (or d...