Roll Number
11I190010
Category
TA
Topics for PhD Qualifiers
1. Optimization
2. Stochastic Process
2. Stochastic Process
Elective1
Title : Convex Optimization
Syllabus : Basic facts of maxima & minima & convex optimization, Important classes of convex optimization problems, Convex sets & convex functions, Differentiable convex functions, Projection on a convex set and normal cone, Sub differential of a convex function, Saddle point Conditions, Karush-kuhn-Tucker Conditions, Lagrangian duality and examples, Strong duality & consequences, Linear programming, basics & examples, Basic results and the fundamental theorems of linear programming.
Syllabus : Basic facts of maxima & minima & convex optimization, Important classes of convex optimization problems, Convex sets & convex functions, Differentiable convex functions, Projection on a convex set and normal cone, Sub differential of a convex function, Saddle point Conditions, Karush-kuhn-Tucker Conditions, Lagrangian duality and examples, Strong duality & consequences, Linear programming, basics & examples, Basic results and the fundamental theorems of linear programming.
Elective2
Title : Integer Programming
Syllabus : Effective modelling in integer programming, Optimality, Relaxation, Branch-and-bound, Preprocessing of formulations, Polyhedra and integer programming, Affine independence, Dimensions and faces of polyhedra, Facets of a polyhedra, Cutting plane methods, Different types of valid cuts, Valid inequalities.
Syllabus : Effective modelling in integer programming, Optimality, Relaxation, Branch-and-bound, Preprocessing of formulations, Polyhedra and integer programming, Affine independence, Dimensions and faces of polyhedra, Facets of a polyhedra, Cutting plane methods, Different types of valid cuts, Valid inequalities.
PhD. Supervisor (if decided)
Prof. Ashutosh Mahajan
Proposed Research Plan (if decided)
Global Optimization