Combinatorial Programming: Methods and Applications

Combinatorial n-fold Integer Programming and Applications

Integer Linear Programming is a famous NP-complete problem. Lenstra showed that in the case of small dimension, it can be solved in polynomial time. This algorithm became a ubiquitous tool, especially in the design of parameterized algorithms for NP-complete problems, where we wish to isolate the hardness of an instance to some parameter. However, it was discovered that in many cases using Lens...

Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization

We study the semideenite programming problem (SDP), i.e the optimization problem of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semideenite. First we review the classical cone duality as is specialized to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomi...

Linear, Semidefinite Programming and Randomization Methods for Combinatorial Optimization Problems

Generative programming - methods, tools and applications

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Generalized Goal Programming: polynomial methods and applications

In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework. In spite of its generality, this probl...