Inverse optimization is the problem of determining values missing input parameters for an associated forward that are closest to given estimates and will make a target vec...

Minimizing a convex function over the integral points of a bounded convex set is polynomial in fixed dimension [6]. We provide an alternative, short, and geometrically motivated proof of this result. In particular, we present an oraclepolynomial algorithm based on a mixed integer linear optimization oracle.

A linear time-varying aggregate traffic flowmodel can be used to develop traffic flowmanagement strategies using optimization algorithms. However, there are few methods available in the literature to translate these aggregate solutions into practical control actions involving individual aircraft. In this paper, a computationally efficient disaggregation algorithm is proposed by employing a seri...

multi-objective optimization is the simultaneous consideration of two or more objective functions that are completely or partially inconflict with each other. the optimality of such optimizations is largely defined through the pareto optimality. multiple objective integer linear programs (moilp) are special cases of multiple criteria decision making problems. numerous algorithms have been desig...

Solving mixed integer linear programming (MILP) problems is a difficult task due to the parallel use of both integer and non-integer values. One of the most widely used solution is to solve the problem in the real space and they apply additional iteration steps (so-called cutting-plane algorithms or Gomory’s cuts) to narrow down the solution to the optimal integer solution. The ABS class of alg...

Automatic verification of computer code is of paramount importance in embedded systems supplying essential services. One of the most important verification techniques is static code analysis by abstract interpretation: the concrete semantics of a programming language (i.e. values χ that variable symbols x appearing in a program can take during its execution) are replaced by abstract semantics (...

Two independent proofs of the polyhedrality of the split closure of Mixed Integer Linear Program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel.