In this paper we continue the investigations in GMW92a] for the Stei-ner tree packing polyhedron. We present several new classes of valid inequalities and give suucient (and necessary) conditions for these inequalities to be facet-deening. It is intended to incorporate these inequalities into an existing cutting plane algorithm that is applicable to practical problems arising in the design of e...

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they define facets of this polytope. This answers a question posed by Qi and Sun [21]. Moreover, we show that we can separate these inequalities in polynomial time. Finally, we assess the computational...

In this paper we use facets of simple mixed-integer sets with three variables to derive a parametric family of valid inequalities for general mixed-integer sets. We call these inequalities two-step MIR inequalities as they can be derived by applying the simple mixed-integer rounding (MIR) principle of Wolsey (1998) twice. The two-step MIR inequalities define facets of the master cyclic group po...

The max-cut and stable set problems are two fundamental NP -hard problems in combinatorial optimization. It has been known for a long time that any instance of the stable set problem can be easily transformed into a max-cut instance. Moreover, Laurent, Poljak, Rendl and others have shown that any convex set containing the cut polytope yields, via a suitable projection, a convex set containing t...

We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst-case improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor greater than ~. The corresponding factor for the class of clique tree inequalities is 8, while it i...

We consider a network design problem that arises in the costoptimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design problem and the single-source capacitated facility location problem We refer to it as the Capacitated Con...

Laurent & Poljak introduced a class of valid inequalities for the max-cut problem, called gap inequalities, which include many other known inequalities as special cases. The gap inequalities have received little attention and are poorly understood. This paper presents the first ever computational results. In particular, we start presenting a cuttingplane scheme based on an effective heuristic s...

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint ove...

As renewable energy penetration rates continue to increase in power systems worldwide, newchallenges arise for system operators in both regulated and deregulated electricity markets tosolve the security constrained unit commitment problem with intermittent generation (due torenewables) and uncertain load, in order to ensure system reliability and maintain cost effec-tiveness. In...

A conditional lower bound on the minimand of an integer program is a number which would be a valid lower bound if the constraint set were amended by certain inequalities, also called conditional. If such a conditional lower bound exceeds some known upper bound, then every solution better than the one corresponding to the upper bound violates at least one of the conditional inequalities. This yi...