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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
14.
Computational Aspects and Software
14.1.
Numerical Considerations
14.1.1.
Floating Point Arithmetic
14.1.2.
Conditioning and Stability
14.1.3.
Scaling and Preconditioning
14.1.4.
Convergence Criteria
14.2.
Algorithm Implementation
14.2.1.
Data Structures
14.2.2.
Memory Management
14.2.3.
Parallel Computing
14.2.4.
GPU Acceleration
14.3.
Software Tools and Libraries
14.3.1.
Modeling Languages
14.3.1.1.
AMPL
14.3.1.2.
GAMS
14.3.1.3.
Pyomo
14.3.2.
Solver Interfaces
14.3.3.
Commercial Solvers
14.3.4.
Open Source Solvers
14.4.
Performance Analysis
14.4.1.
Computational Complexity
14.4.2.
Benchmarking
14.4.3.
Profiling and Optimization
14.4.4.
Scalability Analysis
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13. Applications and Case Studies
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1. Foundations of Optimization