Continuous and discrete optimization techniques for some problems in industrial engineering and materials design

This work comprises several projects that involve optimization of physical systems. By a physical system we understand an object or a process that is governed by physical, mechanical, chemical, biological, etc., laws. Such objects and the related optimization problems are relatively rarely considered in operations research literature, where the traditional subjects of optimization methods are represented by schedules, assignments and allocations, sequences, and queues. The corresponding operations research and management sciences models result in optimization problems of relatively simple structure (for example, linear or quadratic optimization models), but whose difficulty comes from very large number (from hundreds to millions) of optimization variables and constraints. In contrast, in many optimization problems that arise in mechanical engineering, chemical engineering, biomedical engineering, the number of variables or constraints in relatively small (typically, in the range of dozens), but the objective function and constraints have very complex, nonlinear and nonconvex analytical form. In many problems, the analytical expressions for objective function and constraints may not be available, or are obtained as solutions of governing equations (e.g., PDE-onstrained optimization problems), or as results of external simulation runs (black-box optimization). In this dissertation we consider problems of classification of biomedical data, construction of optimal bounds on elastic tensor of composite materials, multiobjective (multi-property) optimization via connection to stochastic orderings, and black-box combinatorial optimization of crystal structures of organic molecules.