Chapter 1. Introduction and Preliminaries
1.1. Introduction.
1.2. Basic Notations and Terminologies
1.3. Optimality Conditions
1.4. Line Search
1.5. A Remark
Chapter 2. Slope Lemmas
2.1. The First Slope Lemma
2.2. An Example
2.3. Gradient Projection on Tangent Plane
2.4. The Second Slope Lemma
Chapter 3. Rosen's Method and Its Convergence
3.1. Rosen's Method
3.2. Choice of Parameter
3.3. Global Convergence
3.4. Rate of Convergence
3.5. Kantorovich Inequality
3.6. Degeneracy
Chapter 4. Combining with Variable Metric Methods
4.1. A Variation of Goldfarb's Method
4.2. Pu-Yu's Theorem
Chapter 5. e-Active Set Strategy..
5.1. Decomposition of Polyhedron
5.2. Stability of Regularity (I)
5.3. An Example
5.4. Stability of Regularity (II)
5.5. Rotating Tangent Plane
Chapter 6. Reduced Gradient Methods
6.1. Wolfe's Method
6.2. Nondegeneracy Assumption
6.3. Yue-Han's Pivot
6.4. Convergence of Wolfe's Method
6.5. Luenberger's and Wang's Variations
6.6. Improving Rosen's Method
Chapter 7. Point-to-Set Mapping
7.1. Zangwill's Theorem
7.2. Consequences of Slope Lemmas
7.3. Comparison
Chapter 8. On Other Topics
8.1. The Third Slope Lemma
8.2. Ritter's Rule and Its Extension
8.3. Global Convergence Rate
8.4. Karmarkar's Alogrithm
8.5. Nonsmooth Optimization
References