Unconstrained Optimization : Basic properties of solutions and algorithms, Global convergence.
Basic Descent Methods : Line Search Methods, Steepest Descent and Newton Methods,Modified Newton methods, Globally convergent Newton Method,Nonlinear Least Squares Problem and Algorithms,Conjugate Direction Methods,Trust-Region Methods.
Constrained Optimization : First Order Necessary Conditions, Second Order Necessary Conditions, Duality, Constraint Qualification,Convex Programming Problem and Duality.
Linear Programming : The Simplex Method, Duality and Interior Point Methods, Karmarkar's algorithm,Transportation and Network flow problem.
Quadratic Programming : Active set methods, Gradient Projection methods and sequential quadratic programming.
Dual Methods : Augmented Lagrangians and cutting-plane methods,Penalty and Barrier Methods,Interior Point Methods.
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Introduction
Preview 00:53:32
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Mathematical Background
00:55:44
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Mathematical Background I
00:58:51
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One Dimensional Optimization - Optimality Conditions
00:56:02
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One Dimensional Optimization I
01:08:19
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Convex Sets
00:43:58
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Convex Sets I
00:56:10
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Convex Functions II
00:56:25
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Convex Functions III
01:16:29
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Optimality Conditions, Conceptual Algorithm
00:36:34
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Line Search Techniques
00:57:01
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Global Convergence Theorem
00:57:36
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Steepest Descent Method
00:57:10
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Classical Newton Method
00:57:35
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Trust Region and Quasi-Newton Methods
00:57:02
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Quasi-Newton Methods - Rank One Correction, DFP Method
00:57:30
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Quasi-Newton Methods - Rank One Correction, DFP Method I
00:54:40
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Conjugate Directions
00:56:24
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Quasi-Newton Methods - Rank One Correction, DFP Method II
00:55:39
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Constrained Optimization - Local&Global,Conceptual Algorithm
00:56:57
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Feasible and Descent Directions
00:57:03
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First Order KKT Conditions
00:58:21
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Constraint Qualifications
00:56:33
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Convex Programming Problem IV
00:55:19
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Second Order KKT Conditions
00:55:10
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Second Order KKT Conditions 1
00:50:52
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Weak and Strong Duality
00:55:21
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Geometric Interpretation
00:55:47
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Lagrangian Saddle Point and Wolfe Dual
01:22:31
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Linear Programming Problem
00:30:46
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Geometric Solution
00:57:22
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Basic Feasible Solution
00:57:17
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Optimality Conditions and Simplex Tableau
00:57:41
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Simplex Algorithm and Two-Phase Method
00:58:00
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Duality in Linear Programming
00:58:19
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Interior Point Methods - Affine Scaling Method
00:58:10
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Karmarkars Method
01:24:30
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Lagrange Methods, Active Set Method
00:29:27
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Active Set Method 1
00:57:48
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Barrier& Penalty,Augmented Lagrangian &Cutting Plane Method
00:32:47
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Summary
00:20:42
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