The quadratic traveling salesman problem asks for a tour of min-imal costs where the costs are associated with each two arcs that are traversedin succession. This structure arises, e. g., if the succession of two arcs representsthe costs of loading processes in transport networks or a switch between dif-ferent technologies in communication networks. Based on a quadratic integer<...

We consider variational inequalities with different trial and test spaces and a possibly non-coercive bilinear form. Well-posedness is shown under general conditions that are e.g. valid for the space-time variational formulation of parabolic variational inequalities. Moreover, we prove an estimate for the error of a Petrov-Galerkin approximation in terms of the residual. For parabolic variation...

AbstractTheoretical results relating to the facial structure of the general binary integer-programming polytope conv({x ∈ {0, 1} : Ax ≤ b}) where A ∈ r n × R , and b ∈R are presented. A conflict hypergraph is constructed and some induced hyperstars create valid inequalities of . BIP P These inequalities are further shown to produce large dimensional faces. Some computational results show the b...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

In this paper, a comprehensive model for hub location-routing problem is proposed which no network structure other than connectivity is imposed on backbone (i.e. network between hub nodes) and tributary networks (i.e. networks which connect non-hub nodes to hub nodes). This model is applied in public transportation, telecommunication and banking networks. In this model locating and routing is c...

This paper establishes a foundation for a cutting plane approach to solve a class of problems that are important to assembly systems, including assembly line balancing (ALB), workload smoothing (WS) and assembly system design (ASD). We describe relationships among the integer programming formulations of these problems and recast their relaxations as node packing problems (NPPs). Exploiting the ...

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide ran...

One-dimensional infinite group problems have been extensively studied and have yielded strong cutting planes for mixed integer programs. Although numerical and theoretical studies suggest that group cuts can be significantly improved by considering higher-dimensional groups, there are no known facets for infinite group problems whose dimension is larger than two. In this paper, we introduce an ...

A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas as finance, location, and scheduling. Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that relate the continuous ...

A separation heuristic for mixed integer programs is presented that theoretically allows one to derive several families of “strong” valid inequalities for specific models and computationally gives results as good as or better than those obtained from several existing separation routines including flow cover and integer cover inequalities. The heuristic is based on aggregation of constraints of ...