Towards Large Scale Deterministic Global Optimization
In this presentation, we will provide an overview of the research progress in global optimization. The focus will be on important contributions during the last five years, and will provide a perspective for future research opportunities. The overview will cover the areas of (a) twice continuously differentiable constrained nonlinear optimization, and (b) mixed-integer nonlinear optimization models. Subsequently, we will present our recent fundamental advances in (i) convex envelope results for multi-linear functions, (ii) a piecewise quadratic convex underestimator for twice continuously differentiable functions, (iii) piecewise linear relaxations of bilinear functions, (iv) large scale extended pooling problems, and (v) large scale generalized pooling problems. Computational studies on medium and large scale global optimization applications will illustrate the potential of these advances.