MTH424: Convex Analysis (Spring 2025)

Convex Analysis Convex analysis is a branch of mathematics that studies convex sets and convex functions. A set is convex if a straight line between any two points in the set always stays inside it. This field is important in optimization, economics, and engineering. It helps in solving real-world problems like minimizing costs, maximizing profits, and designing efficient systems. Convex analysis is widely used in machine learning, finance, and physics. 😊

Course Objectives

✅ Understanding Convex Analysis

Learn the basic concepts of convex sets and convex functions.

✅ Exploring Convex Functions

Study the differential properties of convex functions.

✅ Hadamard-Hermite Inequalities

Understand these inequalities and their real-world applications.

✅ Enhancing Mathematical Skills

Improve logical thinking through homework and projects.

✅ Developing Self-Independent Learning

Gain confidence in solving mathematical problems independently.

This course will strengthen your mathematical foundation and problem-solving abilities! 😊

Course Contents

Convex sets and their properties, Convex hull and their properties, Best approximation theorem. Convex functions, Basic definitions, properties, various generalizations, Differentiable convex functions, Hermite and Hadamard inequalities, Subgradient, Characterizations and applications in linear and nonlinear optimization.

Quizzes and Assignments

Please click on View Online to see inside the PDF.

Online Resources

  1. Roberts, A. W., & Varberg, D. E. (1973). Convex functions. Academic Press. (Google Book Preview)
  2. Rockafellar, R. T. (1970). Convex analysis. Princeton University Press. (Google Book Preview)
  3. Bauschke, H. H., & Combettes, P. L. (2011). Convex analysis and monotone operator theory in Hilbert spaces. Springer.
  4. Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (2006). Nonlinear programming: Theory and algorithms (3rd ed.). Wiley-Interscience.
  5. Niculescu, C. P., & Persson, L. E. (2006). Convex functions and their applications: A contemporary approach. Springer.