Convex optimization under combinatorial sparsity constraints

We present a heuristic approach for convex optimization problems containing sparsity constraints. The latter can be cardinality constraints, but our approach also covers more complex constraints on the support of the solution. For the special case that the support is required to belong to a matroid, we propose an exchange heuristic adapting the support in … Read more

On Lexicographic Approximations of Integer Programs

We use the lexicographic order to define a hierarchy of primal and dual bounds on the optimum of a bounded integer program. These bounds are constructed using lex maximal and minimal feasible points taken under different permutations. Their strength is analyzed and it is shown that a family of primal bounds is tight for any … Read more

Matroid Optimization Problems with Monotone Monomials in the Objective

In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. … Read more