- Convex Optimization Tutorial
- Home
- Introduction
- Linear Programming
- Norm
- Inner Product
- Minima and Maxima
- Convex Set
- Affine Set
- Convex Hull
- Caratheodory Theorem
- Weierstrass Theorem
- Closest Point Theorem
- Fundamental Separation Theorem
- Convex Cones
- Polar Cone
- Conic Combination
- Polyhedral Set
- Extreme point of a convex set
- Direction
- Convex & Concave Function
- Jensen's Inequality
- Differentiable Convex Function
- Sufficient & Necessary Conditions for Global Optima
- Quasiconvex & Quasiconcave functions
- Differentiable Quasiconvex Function
- Strictly Quasiconvex Function
- Strongly Quasiconvex Function
- Pseudoconvex Function
- Convex Programming Problem
- Fritz-John Conditions
- Karush-Kuhn-Tucker Optimality Necessary Conditions
- Algorithms for Convex Problems

- Convex Optimization Resources
- Convex Optimization - Quick Guide
- Convex Optimization - Resources
- Convex Optimization - Discussion

- Selected Reading
- UPSC IAS Exams Notes
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This tutorial will introduce various concepts involved in non-linear optimization. Linear programming problems are very easy to solve but most of the real world applications involve non-linear boundaries. So, the scope of linear programming is very limited. Hence, it is an attempt to introduce the topics like convex functions and sets and its variants, which can be used to solve the most of the worldly problems.

This tutorial is suited for the students who are interested in solving various optimization problems. These concepts are widely used in bioengineering, electrical engineering, machine learning, statistics, economics, finance, scientific computing and computational mathematics and many more.

The prerequisites for this course is introduction to linear algebra like introduction to the concepts like matrices, eigenvectors, symmetric matrices; basic calculus and introduction to the optimization like introduction to the concepts of linear programming.

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