Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path

Two corrector-predictor interior point algorithms are proposed for solving mono\-tone linear complementarity problems. The algorithms produce a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm … Read more

Towards nonsymmetric conic optimization

In this paper we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cones. We suggest using the primal correction process to find a {\em scaling point}. This point is used to compute a strictly feasible primal-dual pair by simple projection. Then, we define … Read more

Packing and Partitioning Orbitopes

We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal sub ject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain … Read more

OSiL: An Instance Language for Optimization

Distributed computing technologies such as Web Services are growing rapidly in importance in today’s computing environment. In the area of mathematical optimization, it is becoming increasingly common to separate modeling languages from optimization solvers. In fact, the modeling language software, solver software, and data used to generate a model instance might reside on different machines … Read more

A unified approach for inversion problems in intensity-modulated radiation therapy

We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc.) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that … Read more

Nonserial dynamic programming and local decomposition algorithms in discrete programming

One of perspective ways to exploit sparsity in the dependency graph of an optimization problem as J.N. Hooker stressed is nonserial dynamic programming (NSDP) which allows to compute solution in stages, each of them uses results from previous stages. The class of discrete optimization problems with the block-tree-structure matrix of constraints is considered. Nonserial dynamic … Read more

On forests, stable sets and polyhedras associated with clique partitions

Let $G=(V,E)$ be a simple graph on $n$ nodes. We show how to construct a partial subgraph $D$ of the line graph of $G$ satisfying the identity: $\overline \chi(G)+\alpha(D)=n$, where $\overline \chi(G)$ denotes the minimum number of cliques in a clique partition of $G$ and $\alpha(D)$ denotes the maximum size of a stable set of … Read more

A Particle Swarm Pattern Search Method for Bound Constrained Nonlinear Optimization

In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search … Read more

On the Quality of a Semidefinite Programming Bound for Sparse Principal Component Analysis

We examine the problem of approximating a positive, semidefinite matrix $\Sigma$ by a dyad $xx^T$, with a penalty on the cardinality of the vector $x$. This problem arises in sparse principal component analysis, where a decomposition of $\Sigma$ involving sparse factors is sought. We express this hard, combinatorial problem as a maximum eigenvalue problem, in … Read more

The p-median polytope of restricted Y-graphs

We further study the effect of odd cycle inequalities in the description of the polytopes associated with the p-median and uncapacitated facility location problems. We show that the obvious integer linear programming formulation together with the odd cycle inequalities completely describe these polytopes for the class of restricted Y-graphs. This extends our results for the … Read more