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Systems Science
Operations Research
1. Introduction to Operations Research
2. Mathematical Preliminaries
3. Linear Programming
4. Transportation and Assignment Problems
5. Network Optimization Models
6. Integer Programming
7. Nonlinear Programming
8. Dynamic Programming
9. Stochastic Processes and Markov Chains
10. Queueing Theory
11. Inventory Theory
12. Simulation
13. Decision Analysis
14. Heuristics and Metaheuristics
7.
Nonlinear Programming
7.1.
Introduction to Nonlinear Optimization
7.1.1.
Types of Nonlinearities
7.1.2.
Challenges in Nonlinear Programming
7.1.3.
Local vs. Global Optimization
7.2.
Unconstrained Optimization
7.2.1.
Optimality Conditions
7.2.1.1.
First-Order Necessary Conditions
7.2.1.2.
Second-Order Sufficient Conditions
7.2.2.
Line Search Methods
7.2.2.1.
Steepest Descent Method
7.2.2.2.
Newton's Method
7.2.2.3.
Quasi-Newton Methods
7.2.3.
Trust Region Methods
7.2.4.
Conjugate Gradient Methods
7.3.
Constrained Optimization
7.3.1.
Types of Constraints
7.3.1.1.
Equality Constraints
7.3.1.2.
Inequality Constraints
7.3.2.
Lagrange Multiplier Method
7.3.3.
Karush-Kuhn-Tucker Conditions
7.3.4.
Penalty and Barrier Methods
7.3.5.
Sequential Quadratic Programming
7.4.
Convex Optimization
7.4.1.
Convex Sets and Functions
7.4.2.
Properties of Convex Problems
7.4.3.
Global Optimality in Convex Problems
7.4.4.
Duality in Convex Programming
7.4.5.
Interior Point Methods
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8. Dynamic Programming