## Convergence Analysis of a Long-Step Primal-Dual Infeasible Interior-Point LP Algorithm Based on Iterative Linear Solvers

In this paper, we consider a modified version of a well-known long-step primal-dual infeasible IP algorithm for solving the linear program $\min\{c^T x : Ax=b, \, x \ge 0\}$, $A \in \Re^{m \times n}$, where the search directions are computed by means of an iterative linear solver applied to a preconditioned normal system of equations. … Read more

## Lift-and-project for 0–1 programming via algebraic geometry

Recently, tools from algebraic geometry have been successfully applied to develop solution schemes for new classes of optimization problems. A central idea in these constructions is to express a polynomial that is positive on a given domain in terms of polynomials of higher degree so that its positivity is readily revealed. This resembles the “lifting” … Read more

## Parallel Strategies for GRASP with path-relinking

A Greedy Randomized Adaptive Search Procedure (GRASP) is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and local search. Path-relinking is an intensification strategy that explores trajectories that connect high quality solutions. We analyze two parallel strategies for GRASP with path-relinking and propose a criterion … Read more

## The Network Packing Problem in Terrestrial Broadcasting

The introduction of digital technology all over Europe requires a complete and challenging re-planning of the actual terrestrial broadcasting system. In fact, in order to implement digital networks, transmitters and frequencies must be removed from the current analog networks. On the other hand, the service level (territory coverage) of analog networks must be preserved until … Read more

## A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization

Let $f$ be a continuous function on $\Rl^n$, and suppose $f$ is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which $f$ is not differentiable. Of particular interest is the case where $f$ is not convex, and perhaps not even locally Lipschitz, but … Read more

## A Multi-Exchange Local Search Algorithm for the Capacitated Facility Location Problem

We present a multi-exchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between $3+2\sqrt{2}-\epsilon$ and $3+2\sqrt{2}+\epsilon$ for any given constant … Read more

## Complete Search in Continuous Global Optimization and Constraint Satisfaction

This survey covers the state of the art of techniques for solving general purpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques that provably find all solutions (if there are finitely many). The core of the material is presented in sufficient detail that the survey may serve as a … Read more

## New criss-cross type algorithms for linear complementarity problems with sufficient matrices

We generalize new criss-cross type algorithms for linear complementarity problems (LCPs) given with sufficient matrices. Most LCP solvers require apriori information about the input matrix. The sufficiency of a matrix is hard to be checked (no polynomial time method is known). Our algorithm is similar to Zhang’s linear programming, and Akkeleº-Balogh-Illés’s criss-cross type algorithm for … Read more

## The Reduced Density Matrix Method for Electronic Structure Calculations and the Role of Three-Index Representability Conditions

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used $P$, $Q$ and $G$ conditions. The additional conditions (called $T1$ and $T2$ here) are implicit in work of R.~M.~Erdahl [Int.\ J.\ Quantum Chem.\ {\bf13}, 697–718 (1978)] and extend the well-known three-index diagonal … Read more

## Stable Matchings for A Generalized Marriage Problem

We show that a simple genralization of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley(1962), yeilds outcomes for a generalized marriage problem, which are necessarily stable. We also show, that any outcome of this prcedure is Weakly Pareto Optimal for Men, i.e., there is no other outcome which all men prefer … Read more