MTL625: Principles of Optimization Theory

3 Credits (3-0-0)

Convex set, hyperplane, relative interior and closure, separation theorems, theorems of alternatives for linear systems, convex functions and properties of continuity, differentiability etc., quasiconvex and pseudoconvex functions and their properties and interrelationships, minimax theorems for convex and quasiconvex functions, nonlinear programming, Lagrange function, saddle point, Fritz John optimality conditions, constraint qualifications, KarushKuhn-Tucker (KKT) necessary and sufficient optimality conditions, Wolfe and Mond-Weir duals, Wolfe method for quadratic programs, Projection gradient method, steepest descent method, conjugate gradient method, rank-1 methods, convergence, conjugate function, Fenchel duality, subgradient and subdifferential, nonsmooth optimization, tangent cone, normal cone, nonsmooth KKT conditions, nonsmooth optimality conditions, subgradient method, proximal method, convergence of these methods, applications to support vector machines optimization problems.