New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Retro-Neoliberalism: Elite Counter-Protest in Latin America, 1940-1975

This research challenges the origin story of neoliberalism in Latin America. Drawing on archival data from the Mont Pèlerin Society and the personal archives of leading but neglected figures in the post-war push to rebuild economic liberalism, I present a historical geography of elite counter-protest that both predates and broadens the generally accepted “birth” of neoliberalism in 1970s Chile. Beginning in the 1940s, Latin American elites found common cause with key figures from economic liberalism’s most radical wing: the Austrian School. While existing literature links the onset of neoliberalism in Chile to the Austrian School, particularly with respect to the School’s influence on the early Mont Pèlerin Society, this dissertation is the first comprehensive inquiry to place the Austrian tradition in the ideational and organizational landscape of Latin America. Embracing a new mission that promised to save the soul of Western civilization, Latin America’s retro-neoliberal leaders collaborated with transnational actors to build a network of Austrian-inspired think-tanks and institutes of higher learning in the region. These organizations, in turn, served as recruiting mechanisms to found the Hispanic quarter of the Mont Pèlerin Society, which was dominated not (as might be assumed) by Chileans, but rather by retro-neoliberal elites from Mexico, Argentina, Guatemala, and Venezuela. By 1975, when scholars began analyzing how a run-of-the-mill economics department had been transformed into a bastion of free-market thinking in Chile, an entire neoliberal university was up and running in Guatemala, exposing all students, regardless of discipline, to the Austrian tradition – the crowning achievement of Latin America’s retro-neoliberal network. Investigating, and accounting for, the development and impact of this initiative sheds new light on the neoliberal landscape in Latin America, and raises important questions for the study of neoliberalism more broadly.