Linear and Convex Optimization. Michael H. Veatch
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Название: Linear and Convex Optimization
Автор: Michael H. Veatch
Издательство: John Wiley & Sons Limited
Жанр: Математика
isbn: 9781119664055
isbn:
19 14 Convex Programming: Optimality Conditions 14.1 KKT Optimality Conditions 14.2 Lagrangian Duality
20 15 Convex Programming: Algorithms 15.1 Convex Optimization Models 15.2 Separable Programs 15.3 Unconstrained Optimization 15.4 Quadratic Programming 15.5 Primal‐dual Interior Point Method
21 A Linear Algebra and Calculus Review A.1 Sets and Other Notation A.2 Matrix and Vector Notation A.3 Matrix Operations A.4 Matrix Inverses A.5 Systems of Linear Equations A.6 Linear Independence and Rank A.7 Quadratic Forms and Eigenvalues A.8 Derivatives and Convexity
22 Bibliography
23 Index
List of Tables
1 Chapter 1Table 1.1 Data for sending aid.
2 Chapter 2Table 2.1 Data for Kan Jam production.Table 2.2 Data for auto parts production.Table 2.3 Data for Custom Tees ads.Table 2.4 Data for producing steel.Table 2.5 Solution for producing steel.Table 2.6 Requirements and costs for police shifts.Table 2.7 Demand and labor available for gift basketsTable 2.8 Transmission costs, supply, and demand.Table 2.9 Soybean shipping costs, supply, and demand.
3 Chapter 4Table 4.1 Languages and costs for translators.Table 4.2 Processing times for interventions against an intruder.Table 4.3 Mileage between cities.
4 Chapter 7Table 7.1 Basic solutions for Example 7.6.
5 Chapter 8Table 8.1 Dual relationships.Table 8.2 Possibilities when solving the primal and the dual.Table 8.3 When Systems 1 and 2 have solutions.
6 Chapter 9Table 9.1 Reduced costs and simplex directions for Example 9.5.
7 Chapter 10Table 10.1 General terminology for a linear program.Table 10.2 Sign of shadow prices.Table 10.3 Data for Kan Jam production.Table 10.4 Data for Custom Tees ads.
8 Chapter 11Table 11.1 Dual relationships for corresponding basic solutions.Table 11.2 Iterations of the path following algorithm.Table 11.3 Points on central path.
List of Illustrations
1 Chapter 1Figure 1.1 Region satisfying constraints for sending aid.Figure 1.2 Optimal point and contour for sending aid.Figure 1.3 Problem has optimal solution for dashed objective but is unbounde...Figure 1.4 Feasible integer solutions for (1.5).
2 Chapter 2Figure 2.1 Electricity transmission network.Figure 2.2 Transportation network for soybeans.Figure 2.3 Water pipe network for Exercise 2.25.
3 Chapter 3Figure 3.1 Profit contribution (the negative of cost) for labor.Figure 3.2 Street grid. Each block is labeled with its travel time and each ...Figure 3.3 Travel times for Exercise 3.12.Figure 3.4 Project costs for Exercise 3.13.
4 Chapter 4Figure 4.1 A piecewise linear function.
5 Chapter 5Figure 5.1 An improving direction for maximizing
6 Chapter 6Figure 6.1 Feasible region and isocontours for Example 6.1.Figure 6.2 The first set is convex. The second is not.Figure 6.3 The point
7 Chapter 7Figure 7.1 Basic solutions for Example 7.1.Figure 7.2 The point
8 Chapter 8Figure СКАЧАТЬ