Aykut Ahlatçıoğlu The Convex Hull Heuristic (CHH) is a heuristic for mixed-integer programming problems with a nonlinear objective function and linear constraints. It is a matheuristic in two ways: it is based on the mathematical programming algorithm called simplicial decomposition, or SD, and at each iteration, one solves a mixed-integer programming problem with a linear objective function … Read more
The behavior of enumeration-based programs for solving MINLPs depends at least in part on the quality of the bounds on the optimal value and of the feasible solutions found. We consider MINLP problems with linear constraints. The convex hull relaxation (CHR) is a special case of the primal relaxation (Guignard 1994, 2007) that is very … Read more
The convex hull relaxation (CHR) method (Albornoz 1998, Ahlatçıoğlu 2007, Ahlatçıoğlu and Guignard 2010) provides lower bounds and feasible solutions (thus upper bounds) on convex 0-1 nonlinear programming problems with linear constraints. In the quadratic case, these bounds may often be improved by a preprocessing step that adds to the quadratic objective function terms which … Read more