Syllabus

Module 1: Overview of linear algebra: Vector space, Matrices and Matrix Algebra, Introduction: Mathematical optimization, Least-squares and linear programming, Convex optimization, Nonlinear optimization. [5 Hours]

Module 2: Convex Sets: Affine and Convex Sets, Operations that Preserve Convexity, General Inequalities, Separating and Supporting Hyperplane. Convex Function: Basic Properties and Examples, Operations that Preserve Convexity, The Conjugate Functions, Quasiconvex Function, Log Concave and Log Convex Function, Convexity With Respect to Generalized Inequalities. [10 Hours]

Module 3: Convex Optimization Problems: Optimization Problems, Convex Optimization, Linear Optimization Problems, Quadratic Optimization Problems, Geometric Programming, Generalized Inequality Constraints, Vector Optimization. [4 Hours]

Module 4: Duality Theory: The Langrage Dual Function, The Langrage Dual Problem, Geometric Interpretation, Saddle Point Interpretation, Optimality Condition, Perturbation and Sensitivity Analysis. [8 Hours]

Module 5: Applications: Norm approximation, Least-norm problems, Regularized approximation, Robust approximation, Function fitting and interpolation. [4 Hours]

Module 6: Algorithms: Unconstrained minimization problems, Descent methods, Gradient descent method, Steepest descent method, Dual Ascent, Dual Decomposition, Augmented Lagrangians and the Method of Multipliers. [5 Hours]

To Understand an optimization problem.

To familiarize with linear and non-linear optimization techniques.

To solve constraint and unconstraint optimization problems.

To learn efficient computational procedures for solving optimization problems.

CO1: Able to understand the basic concepts of linear algebra and optimization techniques.
CO2: Able to explain about convex sets.
CO3: Able to recognize convex functions and convex optimization problems.
CO4: Able to solve unconstrained and constrained optimization problems .
CO5: Able to analyze and apply optimization algorithms.

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press , 2004.

D. P. Palomar and Y. C. Eldar, Convex optimization in signal processing and Communication, Cambridge University Press , 2009.

D. Bertsekas, A. Nedic and A. E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific , 2003.

K. Deb,, Optimization for Engineering Design: Algorithms and Examples, Prentice Hall India Learning Private Limited , 2012.