December 6, 2016
New journal articles on global optimization problems authored by current and former members of PSEL have now appeared online with free access:
- Differentiable McCormick relaxations in Journal of Global Optimization (click here). This article presents a continuously differentiable variant of McCormick’s original relaxations in the multivariate McCormick framework of Tsoukalas and Mitsos. Gradients of the new differentiable relaxations may be computed efficiently using the standard forward or reverse modes of automatic differentiation. Extensions to differentiable relaxations of implicit functions and solutions of parametric ordinary differential equations are discussed. A C++ implementation based on the library MC++ is described and applied to a case study in nonsmooth nonconvex optimization.
- Natural gas production network infrastructure development under uncertainty in Optimization and Engineering (click here). Two scenario-based two-stage stochastic programming models are developed to facilitate natural gas production infrastructure development under uncertainty. One is called the stochastic pooling model, which tracks the qualities of gas streams throughout the production network via a generalized pooling model. The other is an enhancement of the stochastic pooling model with the consideration of pressure. Either model results in a large-scale nonconvex mixed-integer nonlinear programming (MINLP) problem, for which a global optimal solution, although very important for a problem that involves large investments, is very difficult to obtain. A novel optimization method, called nonconvex generalized Benders decomposition (NGBD), is developed for efficient global optimization of the large-scale nonconvex MINLP. Case studies of a real industrial natural gas production system show the advantages of the proposed stochastic programming models over deterministic optimization models, as well as the dramatic computational advantages of NGBD over a state-of-the-art global optimization solver.