DESCRIPTION AND OBJECTIVES

The elegant framework of convex analysis is a powerful integration of key mathematical concepts tied to optimization. It provides a delicate blend of techniques from analysis, topology, and geometry that yields properties of minima and maxima of functions. In this course we shall cover the elements at the heart of convex analysis: Differences of convex functions, Conjugate convex functions and affine sets, we will cover more sophisticated topics from Convex Analysis, such as Convexfunctions on a normed linear space and Differentiability of convex function on normed linear space.

LEARNING OUTCOMES

1. Cope briefly the historical development of the Convex Analysis.
2. Define the Continuity and differentiability of convex functions and evaluate Derivatives some common convex functions.
3. State sufficient conditions under which the Convex function on Normed linear Space exist. 
4. To give students a thorough understanding of how such problems are solved, and some experience in solving them
5. Investigate some applications of the Convex Analysis to the real world.
6. To present the basic theory of such problems, concentrating on results that are useful in computation.

COURSE CONTENTS

1. Convex functions on the real line,
2. Continuity and differentiability of convex functions,
3. Characterizations,
4. Differences of convex functions,
5. Conjugate convex functions,
6. Convex sets and affine sets,
7. Convex functions on a normed linear space,
8. Continuity of convex functions on normed linear space,
9. Differentiable convex function on normed linear space,
10. The support of convex functions,
11. Differentiability of convex function on normed linear space.

Recommended Books

1. Niculescu, C.P. and Persson, L.E., Convex Functions and Their Applications, A Contemporary Approach 2nd ed,(CMS Books in Mathematics(2018)).
2. A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973.

Suggested Books

1. Jonathan M. Borwein and Adrian S. Lewis, Convex Analysis and Nonlinear Optimization: Theory and Examples (CMS Books in Mathematics), 2nd Edition, Springer, 2010.
2. R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, N.J., 1970.
3. J.V. Tiel, Convex Analysis an Introductory Text, John Wiley and Sons, 1984.

Assessment Criteria

       Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

       Mid-Term Exam:   30 (Term paper based)

       Final-Term Exam: 50 (Projects (15) + Viva (25) + Presentation (10)

Key Dates and Time of Class Meeting

Wednesday                                                                            3:30 pm to 5:00 pm

Thursday                                                                                3:30 pm to 5:00 pm

Commencement of Classes                                                   Nonember 02, 2020

Mid Term Examination                                                            December 28 to January 1, 2020

Final Term Examination                                                          March 01-05, 2021

Declaration of Result                                                              March 12, 2021