The truss design problem is to nd the optimal placement and size of structural bars that can support a given load The problem is nonlinear and in the version addressed here the bars must take certain discrete sizes It is shown that a logic based method that dispenses with integer variables and branches directly on logical disjunctions can solve sub stantially larger problems than mixed integer ...

This paper develops a linear programming based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algorithms for mixed integer nonlinear programs in ...

Abstract: A mixed integer programming based approach for optimal control of a class of nonlinear systems with typical non-smooth and even discontinuous components is presented. Firstly, a model denoted as General Linear System Model (GLSM), which can be used to describe accurately a wide range of nonlinear systems with typical nonlinear components, is established. Secondly, based on GLSM, mixed...

This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exp...

Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the into larger decision-making problem, for example, picking best chemical process catalyst. We study large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted penalty functions...

This paper addresses two major issues related to the convergence of generalized Benders decomposition which is an algorithm for the solution of mixed integer linear and nonlinear programming problems. First, it is proved that a mixed integer nonlinear programming formulation with zero nonlinear programming relaxation gap requires only one Benders cut in order to converge, namely the cut corresp...

This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixed-integer nonlinear programs. Towards this end, we develop novel relaxation schemes, range reduction tests, and branching strategies which we incorporate into the prototypical branch-and-bound algorithm. In the theoretical/algorithmic part of the paper, we begin by d...