We propose a modified sequential quadratic programming (SQP) method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is stabilized by a tru...

Mixed integer Gomory cuts have become an integral part of state-of-the-art software for solving mixed integer linear programming problems. Therefore, improvements in the performance of these cutting planes can be of great practical value. In this paper we present a simple and fast heuristic for improving the coefficients on the continuous variables in the mixed integer Gomory cuts. This is moti...

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer programs. In particular, prior to this work, it was open whether some classical problems, like the minimum odd-cut problem, can be expressed by a compact mixe...

Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-inte...

Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe two algorithms that find an -approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithms is polynomial in the size of the problem and in 1/ , provided ...

Recently minimal and extreme inequalities for continuous group relaxations of general mixed integer sets have been characterized. In this paper, we consider a stronger relaxation of general mixed integer sets by allowing constraints, such as bounds, on the free integer variables in the continuous group relaxation. We generalize a number of results for the continuous infinite group relaxation to...

In this paper we present several algorithms which combine a partial enumeration with meta-heuristics for the solution of general mixed-integer programming problems. The enumeration is based on the primal values assignable to the integer variables of the problem. We develop some algorithms for this integration, and test them using a set of well-known benchmark problems. Key-words: Enumeration, L...

We study a generalization of the vertex packing problem having both binary and bounded continuous variables, called the mixed vertex packing problem (MVPP). The well-known vertex packing model arises as a subproblem or relaxation of many 0-1 integer problems, whereas the mixed vertex packing model arises as a natural counterpart of vertex packing in the context of mixed 0-1 integer programming....