IE 331 • Midterm II + Final • Mathematical Modeling and Optimization II

Introduction

Example 1

Example 2

An Important Question

Knapsack Problem and Branch&Bound

Knapsack Problem B&B Example

What is NLP?

Convexity - Single Variable

Convexity - Multivariable

One Variable Unconstrained Optimization

Bisection method

Example 1

Example 2

Newton's method

Example 3

Example 4

Multivariable Unconstrained Optimization

Gradient Search

Example 5

KKT Conditions

Example 1

Reminder: Two-Phase Method

Modified Simplex Method

Example 2

A New Approach to Optimization Problems

Inventory Problems

Example 1

Resource Allocation Problems

Example 2

Solving NLPs with Dynamic Programming

Branch and Bound Method 1

Branch and Bound Method 2

Branch and Bound Method 3

Branch and Bound Method 4

Branch and Bound Method 5

NLP Formulation 1

NLP Formulation 2

Convexity - Single Variable

Convexity - Multivariable 1

Convexity - Multivariable 2

Unconstrained Optimization - Single Variable 1

Unconstrained Optimization - Single Variable 2

Unconstrained Optimization - Multivariable 1

Unconstrained Optimization - Multivariable 2

Unconstrained Optimization - Multivariable 3

Constrained Optimization 1

Constrained Optimization 2

Constrained Optimization 3

Constrained Optimization 4

Constrained Optimization 5

Constrained Optimization 6

Dynamic Programming 1

Dynamic Programming 2

Dynamic Programming 3

Dynamic Programming 4