In this seminar, we will present recent research advances in deterministic global optimization. The focus will be on important theoretical and algorithmic contributions for (a) mixed-integer quadratically constrained quadratic, (MIQCQP), problems; and (b) mixed-integer signomial optimization, (MISO), problems. In Part 1, we will motivate our studies through applications of MIQCQP and MISO. In Part 2, we will present theoretical advances on (i) problem reformulation, (ii) detection of special structure, (iii) detection of convexity, concavity, edge-concavity, (iv) generation of facets of convex and concave envelopes for low-dimensional edge-concave aggregations, (v) piecewise linear underestimation of bilinear terms, (vi) dynamic addition of cuts (RLT, quadratic convex, aBB, high dimensional edge-concave facets), and (vii) a sophisticated branch and bound framework. In Part 3, we will discuss the development of the global optimization solvers GloMIQO and ANTIGONE. Finally, extensive computational studies on medium and large-scale global optimization applications will illustrate the potential of these advances.
Groupe d’études et de recherche en analyse des décisions