Simple Odd $$\beta $$-Cycle Inequalities for Binary Polynomial Optimization

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

On Polynomial Kernels for Structural Parameterizations of Odd Cycle Transversal

TheOdd Cycle Transversal problem (oct) asks whether a given graph can be made bipartite (i.e., 2-colorable) by deleting at most l vertices. We study structural parameterizations of oct with respect to their polynomial kernelizability, i.e., whether instances can be efficiently reduced to a size polynomial in the chosen parameter. It is a major open problem in parameterized complexity whether Od...

Polynomial-Time Separation of Simple Comb Inequalities

Polynomial-Time Separation of Simple Comb Inequalities

The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality...

Optimization on linear matrix inequalities for polynomial systems control

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate approximate solutions in floating point arithmetic. In the first part of the course we describe semidefinite programming (SDP) as an extension of linear progr...