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Numerical Optimization. Instructor: Prof. Shirish K. Shevade, Department of Computer Science and Automation, IISc Bangalore. This course is about studying optimization algorithms, and their applications in different fields.

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September 25, 2023

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Last updated:

September 25, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Numerical Optimization. Instructor: Prof. Shirish K. Shevade, Department of Computer Science and Automation, IISc Bangalore. This course is about studying optimization algorithms, and their applications in different fields.

Mathematical Background: Convex sets and functions, Need for constrained methods in solving constrained problems.
Unconstrained optimization: Optimality conditions, Line Search Methods, Quasi-Newton Methods, Trust Region Methods, Conjugate Gradient Methods, Least Squares Problems.
Constrained Optimization: Optimality Conditions and Duality, Convex Programming Problem, Linear Programming Problem, Quadratic Programming, Dual Methods, Penalty and Barrier Methods, Interior Point Methods. (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Introduction Unlimited
    • Lecture 02 – Mathematical Background Unlimited
    • Lecture 03 – Mathematical Background (cont.) Unlimited
    • Lecture 04 – One Dimensional Optimization – Optimality Conditions Unlimited
    • Lecture 05 – One Dimensional Optimization (cont.) Unlimited
    • Lecture 06 – Convex Sets Unlimited
    • Lecture 07 – Convex Sets (cont.) Unlimited
    • Lecture 08 – Convex Functions Unlimited
    • Lecture 09 – Convex Functions (cont.) Unlimited
    • Lecture 10 – Multidimensional Optimization – Optimality Conditions, Conceptual Algorithm Unlimited
    • Lecture 11 – Line Search Techniques Unlimited
    • Lecture 12 – Global Convergence Theorem Unlimited
    • Lecture 13 – Steepest Descent Method Unlimited
    • Lecture 14 – Classical Newton Method Unlimited
    • Lecture 15 – Trust Region and Quasi-Newton Methods Unlimited
    • Lecture 16 – Quasi-Newton Methods – Rank One Correction, DFP Method Unlimited
    • Lecture 17 – Quasi-Newton Methods – Broyden Family; Coordinate Descent Method Unlimited
    • Lecture 18 – Conjugate Directions Unlimited
    • Lecture 19 – Conjugate Gradient Method Unlimited
    • Lecture 20 – Constrained Optimization – Local and Global Solutions, Conceptual Algorithm Unlimited
    • Lecture 21 – Feasible and Descent Directions Unlimited
    • Lecture 22 – First Order KKT Conditions Unlimited
    • Lecture 23 – Constraint Qualifications Unlimited
    • Lecture 24 – Convex Programming Problem Unlimited
    • Lecture 25 – Second Order KKT Conditions Unlimited
    • Lecture 26 – Second Order KKT Conditions (cont.) Unlimited
    • Lecture 27 – Weak and Strong Duality Unlimited
    • Lecture 28 – Geometric Interpretation Unlimited
    • Lecture 29 – Lagrangian Saddle Point and Wolfe Dual Unlimited
    • Lecture 30 – Linear Programming Problem Unlimited
    • Lecture 31 – Geometric Solution Unlimited
    • Lecture 32 – Basic Feasible Solution Unlimited
    • Lecture 33 – Optimality Conditions and Simplex Tableau Unlimited
    • Lecture 34 – Simplex Algorithm and Two-Phase Method Unlimited
    • Lecture 35 – Duality in Linear Programming Unlimited
    • Lecture 36 – Interior Point Methods – Affine Scaling Method Unlimited
    • Lecture 37 – Karmakar’s Method Unlimited
    • Lecture 38 – Lagrange Method, Active Set Method Unlimited
    • Lecture 39 – Active Set Method (cont.) Unlimited
    • Lecture 40 – Barrier and Penalty Methods, Augmented Lagrangian Method and … Unlimited
    • Lecture 41 – Summary Unlimited

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