Free E-Books: Linear

Linear Ray and Wave Optics in Phase Space: Bridging Ray and Wave Optics via the Wigner Phase-Space Picture

Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ”manifestation” of light, and then corresponds to adequate physical assumptions and formal approximations,
whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.

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Linear Programming : Foundations and Extensions – Lecture Notes

TOC

Part 1: Basic Theory – The Simplex Method and Duality
1. Introduction
2. The Simplex Method
3. Degeneracy
4. Efficiency of the Simplex Method
5. Duality Theory
6. The Simplex Method in Matrix Notation
7. Sensitivity and Parametric Analyses
8. Implementation Issues
9. Problems in General Form
10. Convex Analysis
11. Game Theory
12. Regression

Part 2: Network-Type Problems
13. Network Flow Problems
14. Applications
15. Structural Optimization

Part 3: Interior-Point Methods
16. The Central Path
17. A Path-Following Method
18. The KKT System
19. Implementation Issues
20. The Affine-Scaling Method
21. The Homogeneous Self-Dual Method

Part 4: Extensions
22. Integer Programming
23. Quadratic Programming
24. Convex Programming

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