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Systems Science
Optimization Theory
1. Foundations of Optimization
2. Mathematical Foundations
3. Unconstrained Optimization
4. Constrained Optimization Theory
5. Linear Programming
6. Nonlinear Programming
7. Integer and Combinatorial Optimization
8. Dynamic Programming
9. Stochastic Optimization
10. Heuristic and Metaheuristic Methods
11. Multi-Objective Optimization
12. Specialized Optimization Topics
13. Applications and Case Studies
14. Computational Aspects and Software
12.
Specialized Optimization Topics
12.1.
Convex Optimization
12.1.1.
Conic Programming
12.1.1.1.
Linear Programming as Conic
12.1.1.2.
Second-Order Cone Programming
12.1.1.3.
Semidefinite Programming
12.1.2.
Interior Point Methods for Convex Problems
12.1.3.
Proximal Methods
12.1.3.1.
Proximal Gradient Method
12.1.3.2.
Accelerated Proximal Methods
12.1.4.
Dual Methods
12.1.4.1.
Dual Ascent
12.1.4.2.
Dual Decomposition
12.1.4.3.
ADMM Applications
12.2.
Network Optimization
12.2.1.
Shortest Path Problems
12.2.1.1.
Dijkstra's Algorithm
12.2.1.2.
Bellman-Ford Algorithm
12.2.1.3.
Floyd-Warshall Algorithm
12.2.2.
Maximum Flow Problems
12.2.2.1.
Ford-Fulkerson Algorithm
12.2.2.2.
Push-Relabel Algorithms
12.2.3.
Minimum Cost Flow Problems
12.2.4.
Network Design Problems
12.3.
Game Theory and Optimization
12.3.1.
Nash Equilibrium
12.3.2.
Stackelberg Games
12.3.3.
Cooperative Game Theory
12.3.4.
Mechanism Design
12.4.
Variational Methods
12.4.1.
Calculus of Variations
12.4.2.
Optimal Control Theory
12.4.3.
Pontryagin's Maximum Principle
12.4.4.
Hamilton-Jacobi-Bellman Equation
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11. Multi-Objective Optimization
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13. Applications and Case Studies