Lectures - Optimization

1. Optimization with Inequality Constraints

KKT Conditions

1.1. Example 1

KKT Example 1

1.2. Example 2

KKT Example 2

1.3. Necessity of KKT

KKT Necessity

1.4. Sufficiency of KKT

KKT Sufficiency

2. The Value Function

The Value Function

2.1. Correspondences

UHC and LHC Correspondences

2.2. The Maximum Theorem

The Maximum Theorem

2.3. Concavity and the Maximum Theorem

Maximum theorems and concavity

3. The Envelope Theorem

Envelope Theorem

3.1. Examples

Envelope Examples

4. Fixed Point Theory

Fixed Point Theory

5. OPTIONAL - Duality and Slater's Condition

Slater's Conditions and Strong Duality 1

5.1. OPTIONAL - More Duality

Duality 2