Derivative-free hybrid methods in global optimization and their applications

In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.Doctor of Philosoph

Multicoordination Methods For Solving Convex Block-Angular Programs

Several decomposition methods are considered for solving block-angular programs in parallel. We present a computational comparison of synchronous multicoordination methods. The most efficient of these approaches is shown to involve an intermediate number of blocks in the coordination phase