Invited Session Tue.3.H 2053

Tuesday, 15:15 - 16:45 h, Room: H 2053

Cluster 9: Global optimization [...]

From quadratic through factorable to black-box global optimization


Chair: Leo Liberti



Tuesday, 15:15 - 15:40 h, Room: H 2053, Talk 1

Laurent Dumas
A new global optimization method based on a sparse grid metamodel

Coauthors: Frederic Delbos, Eugenio Echague


A new global optimization method is presented here aimed at solving a general black-box optimization problem where function evaluations are expensive. Our work is motivated by many problems in the oil industry, coming from several domains like reservoir engineering, molecular modeling, engine calibration and inverse problems in geosciences. Even if evolutionary algorithms are often a good tool to solve these problems, they sometimes need too many function evaluations, especially in high-dimension cases. To overcome this difficulty, we propose here a new approach, called SGOM, using the Sparse Grid interpolation method with a refinement process as metamodel.



Tuesday, 15:45 - 16:10 h, Room: H 2053, Talk 2

Christodoulos Achilleus Floudas
Globally optimizing mixed-integer quadratically-constrained quadratic programs (MIQCQP)

Coauthor: Ruth Misener


A general framework for deterministically addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to epsilon-global optimality is introduced. Algorithmic components include: reformulating user input, detecting special mathematical structure, generating tight convex relaxations, dynamically generating cuts, partitioning the search space, bounding variables, and finding feasible solutions.
We also discuss computational experience with the global mixed-integer quadratic optimizer, GloMIQO. New components in GloMIQO include integrating a validated interval arithmetic library, dynamically adding alphaBB cuts and higher-order edge-concave cuts, addressing discrete/discrete and discrete/continuous products, selectively adding
bilinear terms for RLT cuts, and eliminating bilinear terms based on knapsack constraint inferences. Data is presented for globally optimizing a range of MIQCQP including process networks, computational geometry, and quadratic assignment problems.



Tuesday, 16:15 - 16:40 h, Room: H 2053, Talk 3

Angelos Tsoukalas
Extension of McCormick's composition to multi-variate outer functions

Coauthor: Alexander Mitsos


G. P. McCormick [Math Prog 1976] provides the framework for the convex/concave relaxations of factorable functions involving functions of the form Fº f, where F is a univariate function. We give a natural reformulation of McCormick's Composition theorem which allows for a straight forward extension to multi-variate outer functions. In addition to extending the framework, we show how the result can be used in the construction of relaxation proofs.
A direct consequence is an improved relaxation for the product of two functions which is at least as tight and some times tighter than McCormick's result. We also apply the composition result to the minimum/maximum and the division of two functions yielding an improvement on the current relaxation. Finally we interpret McCormick's Composition theorem as a decomposition approach to the auxiliary variable reformulation methods and we introduce some ideas for future hybrid variations.


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