Convex nondifferentiable, also known as convex nonsmooth, optimization (NDO) looks at problems where the functions involved are not continuously different...

Interior-point methods in semi-definite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions...

The analytic center cutting plane method and its proximal variant are well known techniques for solving convex programming problems. We propose two seq...

Convex feasibility problem in general is a problem of finding a point in a convex set contains a full dimensional ball and is contained in a compact convex ...

We present a novel exact solution method for the centralized network design problem on directed graphs. The problem is modelled as the well-known graph theo...

The Analytic Center, Cutting Plane Method for Variational Inequalities with quadratic cuts, ACCPM-VI(quadratic cuts), was introduced in Denault and Goffin,...

We introduce a cutting plane, analytic center algorithm for strongly monotone variational inequalities (VIs). The approach extends that of Goffin, Marcotte...

In this paper, we describe <i>H</i>-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on ...

A variant of method of centers for convex optimization is considered. Given an upper bound on the objective function, the algorithm searches for an "approx...

This paper presents a novel integration of interior point cutting plane methods within branch-and-price algorithms. Unlike the classical method, columns are...

We consider a case of the convex feasibility problem where the set is defined by an infinite number of certain strongly convex self-concordant inequalities....

We analyze an analytic center cutting plane algorithm for the convex feasibility problems with semidefinite cuts. At each iteration the oracle returns a ...

We consider a quadratic cut method based on analytic centers for two cases of convex quadratic feasibility problems. In the first case, the convex set is de...

This article was written for the <i>Encyclopedia of Optimization.</i>

This article was written for the <i>Encyclopedia of Optimization.</i>

We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self...

We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when th...

We study the subgradient projection method for convex optimization with Brännlund's level control for estimating the optimal value. We establish global con...

We describe the analytic center cutting plane method and its relationship to classical methods of nondifferentiable optimization and column generation. Impl...

The paper considers two cases of variational inequality problems. The first case involves an affine monotone operator over a convex set defined by a separat...

We present an algorithm for variational inequalities <i>VI</i>( <img src="G9756.gif" align=bottom>,<i>Y</i>) that is based on the Analytic Center Cutting Pl...

We analyze the process of a two cut generation scheme in the analytic center cutting plane method. We propose an optimal restoration direction when the two...

The analytic center cutting plane (ACCPM) methods aims to solve nondifferentiable convex problems. The technique consists of building an increasingly refine...

In this paper, we explore a weakness of a specific implementation of the analytic center cutting plane method applied to convex optimization problems, which...

The capacitated multi-item lot sizing problem consists of finding a production schedule that minimizes over a finite number of periods the total production,...

The convergence and the complexity of a primal-dual column generation and cutting plane algorithm from approximate analytic centers for solving convex feasi...

This paper describes two interior-point algorithms for solving a class of monotone variational inequalities defined over the intersection of an affine set a...

A cutting plane algorithm for minimizing a convex function subject to constraints defined by a separation oracle is presented. The algorithm is based on app...

The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a pote...

We further analyze the convergence and the complexity of a primal-dual column generation algorithm for solving general convex or quasiconvex feasibility pro...

We analyze the convergence and the complexity of a potential reduction column generation algorithm for solving general convex or quasiconvex feasibility pro...

The stochastic linear programming problem with recourse has a dual block angular structure. It can thus be handled by Benders decomposition or by Kelley's m...

This paper deals with the implementation of the interior point cutting plane algorithm of Goffin-Haurie-Vial, with a special application to the solution of ...

In this paper we propose a path-following, or short-step, version of Karmarkar's algorithm for the primal and for the dual problems. We show it to converge ...

This paper deals with a decomposition technique for linear programs which proposes a new treatment of the master program in the classical Dantzig-Wolfe algo...

The primal projective algorithm for linear programs with unknown optimal objective function value is extended to the case where one uses a weighted Karmarka...

This paper deals with an application of the projective algorithm to the solution of a generic nondifferentiable minimization problem. This problem is closel...

This paper is concerned with the decisions (output decisions and associated sell-or-process-further decisions) that arise with joint products when the techno...

The deepest, or least shallow, cut ellipsoid method is a polynomial (time and space) method which finds an ellipsoid, representable by polynomial space integ...

The space of ellipsoids may be metrized by the Hausdorff distance or by the sum of the distance between their centers and a distance between matrices. Vario...

The ellipsoid method is applied to the unconstrained minimization of a general convex function. The method converges at a geometric rate, which depends only...