Programme PhD Term VI Academic Year 2021-22

Course title Convexity & Optimization Area Production and Quantitative Methods Credits 1.50

Prof. Prahalad Venkateshan

Course Description & Objectives
Develop the theory of convexity as applied to optimization
Convex analysis is the analysis of properties of convex functions and convex sets in a normed vector space. In optimization, convexity plays a very important role in proving
optimality results in both linear and nonlinear optimization. Various separating hyperplane theorems are developed. The sufficiency of KKT conditions for optimality of convex programming problem is proven. To prove the existence of a separating hyperplane between two disjoint convex sets requires knowledge of continuous functions, affine transformations, dimension of sets, hyperplanes and uses other topological properties of sets such as closure, relative interior, relative boundary and compactness, amongst others. This course is aimed at establishing these results from basic results in set theory and topology. Among the topics discussed are basic properties of convex sets, separation theorems, properties of convex functions, mimima and maxima of convex functions over a convex set and various optimization problems.

Lecture, Quizzes, Homework, End Term Examination