COL756: Difference between revisions
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| credits = 3 | | credits = 3 | ||
| credit_structure = 3-0-0 | | credit_structure = 3-0-0 | ||
| pre_requisites = COL351 OR Equivalent | | pre_requisites = [[COL351]] OR Equivalent | ||
| overlaps = MTL103, MTL704 | | overlaps = [[MTL103]], [[MTL704]] | ||
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== COL756 : Mathematical programming == | == COL756 : Mathematical programming == | ||
Linear programming: introduction, geometry, duality, sensitivity analysis. Simplex method, Large scale optimization, network simplex. Ellipsoid method, problems with exponentially many constraints, equivalence of optimization and separation. Convex sets and functions – cones, hyperplanes, norm balls, generalized inequalities and convexity, perspective and conjugate functions. Convex optimization problems – quasi-convex, linear, quadratic, geometric, vector, semi-definite. Duality – Lagrange, geometric interpretation, optimality conditions, sensitivity analysis. Applications to approximation, fitting, statistical estimation, classification. Unconstrained minimization, equality constrained minimization and interior point methods. Integer Programming: formulations, complexity, duality. Lattices, geometry, cutting plane and branch and bound methods. Mixed integer optimization. | Linear programming: introduction, geometry, duality, sensitivity analysis. Simplex method, Large scale optimization, network simplex. Ellipsoid method, problems with exponentially many constraints, equivalence of optimization and separation. Convex sets and functions – cones, hyperplanes, norm balls, generalized inequalities and convexity, perspective and conjugate functions. Convex optimization problems – quasi-convex, linear, quadratic, geometric, vector, semi-definite. Duality – Lagrange, geometric interpretation, optimality conditions, sensitivity analysis. Applications to approximation, fitting, statistical estimation, classification. Unconstrained minimization, equality constrained minimization and interior point methods. Integer Programming: formulations, complexity, duality. Lattices, geometry, cutting plane and branch and bound methods. Mixed integer optimization. | ||
Latest revision as of 16:26, 14 April 2026
| COL756 | |
|---|---|
| Mathematical programming | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | COL351 OR Equivalent |
| Overlaps | MTL103, MTL704 |
COL756 : Mathematical programming
Linear programming: introduction, geometry, duality, sensitivity analysis. Simplex method, Large scale optimization, network simplex. Ellipsoid method, problems with exponentially many constraints, equivalence of optimization and separation. Convex sets and functions – cones, hyperplanes, norm balls, generalized inequalities and convexity, perspective and conjugate functions. Convex optimization problems – quasi-convex, linear, quadratic, geometric, vector, semi-definite. Duality – Lagrange, geometric interpretation, optimality conditions, sensitivity analysis. Applications to approximation, fitting, statistical estimation, classification. Unconstrained minimization, equality constrained minimization and interior point methods. Integer Programming: formulations, complexity, duality. Lattices, geometry, cutting plane and branch and bound methods. Mixed integer optimization.