Learn · A Primer to Mathematical Optimization
Lecture 15 of 42Week 06
Lecture - 17 : First-Order and Second-Order Characterization of Convex Functions
Prof. Debdas Ghosh · IIT(BHU) Varanasi
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- A Primer to Mathematical Optimization, IIT(BHU) Varanasi (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Kanpur.
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All the lectures
- Lecture 01: Introduction and Histroy on the Development of Optimization Theory
- Lecture 02: Tools from Linear Algebra
- Lecture 03: Tools from Linear Algebra
- Lecture 04 : Tools for calculus of several variables
- Lecture 05 : Tools from calculus of several variables
- Lecture 6: Order of Convergence
- Lecture 7: Continuity
- Lecture 8 & 9 : Partial and Directional Derivatives and Differentiability
- Lecture - 10 : Taylor's Theorem
- Lecture - 11 : Convex Sets & Convexity Preserving Operations
- Lecture - 12 : Separation Result
- Lecture - 13 & 14 : Theorems of Alternatives
- Lecture - 15 : Convex Functions
- Lecture -16 : Properties and Zeroth Order Characterization of Convex Functions
- Lecture - 17 : First-Order and Second-Order Characterization of Convex Functions
- Lecture - 18 : Convexity Preserving Operations
- Lecture - 19 : Optimality and Coerciveness
- Lecture 20 part 1: First Order Optimality Condition
- Lecture 20 part 2: Second Order Optimality Conditions
- Lecture 21: General Structure of Unconstrained Optimization Algorithms
- Lecture 22: Inexact Line Search
- Lecture 23 & 24: Global Convergence of Descent Methods
- Lecture 25: Where do Descent Methods Converge?
- Lecture - 26 : Scaling Of Variables
- Lecture - 27 : Practical Stopping Criteria
- Lecture - 28 & 29 : Steepest Descent Method
- Lecture - 30, 31 & 32 : Newton's Method
- Lecture - 33, 34 & 35
- Lecture - 36 & 37
- Lecture - 38 Part 1
- Lecture - 38 Part 2
- Lecture - 39 : A Revisit to Lagrange Multipliears Method
- Lecture - 40 : Special Cones for Contrained Optimization
- Lecture - 41 : Tangent Cone
- Lecture - 42 & 43 : First-Order KKT Optimality Conditions
- Lecture 44 : Second-Order KKT Optimality Conditions
- Lecture 45 : Constraint Qualifications
- Lecture 46, 47, 48, 49 & 50 : Lagrangian Duality Theory
- Lecture 51, 52 & 53 : Methods for Linearly Constrained Problems
- Lecture 54 : Interior-Point Method for QPP
- Lecture 55 : Penalty Methods
- Lecture 56 : Sequential Quadratic Programming Method