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...

Shared memory architectures are gradually becoming more prominent in the HPC market, as advances in technology have allowed larger numbers of CPUs to have access to a single memory space. In addition, manufacturers are increasingly clustering these SMP systems together to go beyond the limits of a single system. As clustered SMPs become more prominent, it becomes more important for applications...

GAMS (General Algebraic Modelling System) is a computer language which was originally developed to assist economists at the World Bank in the quantitative analysis of economic policy questions (Meeraus (1983), Brooke, Kendrick and Meeraus (1987)). At the time of its conception and initial development, linear programming (LP) was the standard framework in which market equilibrium models were con...

In this contribution we apply different approaches to solve four rather different MINLP problems: special extensions to time-indexed formulations of production planning problems, a production planning problem in BASF’s petrochemical division, a site analysis of one of BASF’s bigger sites, and a process design problem. The first problem is related to a useful nonlinear extension of production pl...

This paper presents the solution to a routing problem (Pick-up and Delivery with Time Windows) by Mixed Set Programming which solves constraint satisfaction problems over a mixed domain of reals, integers, Booleans, references and sets [8]. To illustrate the method, a complete constraint program in the NCL language [7, 9] is presented.

In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose th...

A conic integer program is an integer programming problem with conic constraints. Conic integer programming has important applications in finance, engineering, statistical learning, and probabilistic integer programming. Here we study mixed-integer sets defined by second-order conic constraints. We describe general-purpose conic mixed-integer rounding cuts based on polyhedral conic substructure...