A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main advantage of this algorithm is that it automatically and...

Feasibility pump is a general purpose technique for finding feasible solutions of mixed integer programs. In this paper we report our computational experience on using geometric random walks and a random ray approach to provide good points for the feasibility pump. Computational results on <Emphasis...</emphasis>

The paper shows that the global resolution of a general convex quadratic program with complementarity constraints (QPCC), possibly infeasible or unbounded, can be accomplished in finite time. The method constructs a minmax mixed integer formulation by introducing finitely many binary variables,...

This paper presents an algorithm and its implementation in the software package <ExternalRef> <RefSource> <Emphasis FontCategory="NonProportional">NCSOStools </RefSource> <RefTarget Address="http://ncsostools.fis.unm.si/" TargetType="URL"/> </ExternalRef> for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and...</emphasis></refsource></externalref>

We consider a network design problem that arises in the cost-optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design...

We focus in this paper the problem of improving the semidefinite programming (SDP) relaxations for the standard quadratic optimization problem (standard QP in short) that concerns with minimizing a quadratic form over a simplex. We first analyze the duality gap between the standard QP and one of...

In the bottleneck hyperplane clustering problem, given n points in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb{R}^{d}$</EquationSource> </InlineEquation> and an integer k with 1≤k≤n, we wish to determine k hyperplanes and assign each point to a hyperplane so as to minimize the maximum Euclidean distance between each point and its assigned hyperplane. This...</equationsource></inlineequation>

We address the exact solution of general integer quadratic programs with linear constraints. These programs constitute a particular case of mixed-integer quadratic programs for which we introduce in Billionnet et al. (Math. Program., <CitationRef CitationID="CR3">2010</CitationRef>) a general solution method based on quadratic convex...</citationref>

The variable projection algorithm of Golub and Pereyra (SIAM J. Numer. Anal. 10:413–432, <CitationRef CitationID="CR12">1973</CitationRef>) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a...</citationref>

In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the...