Such as linear programming, nonlinear programming, multi-objective programming, dynamic programming, parametric programming, combinatorial optimization and integer programming, stochastic programming, fuzzy programming, nonsmooth optimization, multilevel programming, global optimization, variational inequality and complementarity problems. Widely used in various fields, especially in the financial field.
Basic Introduction Title: Mathematical Planning Author: Huang Hongxuan ISBN: 9787302121770+0770 Pricing: 45 yuan Press: Tsinghua University Press: 2006-3- 1 English Name: Mathematical Programming Book Introduction, Catalog, Book Introduction This book takes mathematical programming as the object, and introduces some methods to analyze and solve common optimization problems from the aspects of theory, algorithm and calculation. The book is divided into eight chapters, of which chapter 1 introduces examples and models of mathematical programming and the basic knowledge involved in analyzing optimization problems. Chapter two to chapter eight discuss seven aspects, namely convex analysis, linear programming, unconstrained optimization, constrained optimization, multi-objective programming, combinatorial optimization, integer programming and global optimization. In addition, the last section of each chapter gives some exercises. At the end of the book, references and indexes are listed. This book can be used as a teaching material for graduate students and senior undergraduates majoring in applied mathematics, computational mathematics, operational research and cybernetics, management science and engineering, industrial engineering and systems engineering to learn mathematical planning. It can also be used as a scientific researcher who needs to use mathematical programming methods to model and solve practical problems in other disciplines. Reference Book Catalogue for Engineers and Technicians Chapter 65438 +0 Introduction 1 1 Topic Introduction 1.2 Examples and Models 4 1.3 Preparatory Knowledge 9 1.3 1 Linear Space 91.0 .3.4 Decomposition and Correction of Matrix 654388+0 Points Separated from Convex Sets 28 2.3.2 Convex Sets Separated from Convex Sets 365,438+0 2.4 Polyhedron Theory 32 2.4.65, 438+0 Polyhedron Dimension 33 2.4.2 Selection Theorem 34 2.4.3 Representation of Faces of Polyhedron and Minimum Inequality 38 2.4.4 Representation Theorem of Polyhedron 44 2.5 Convex Function 49 2.5 5 5.2 Judgment Method of Convexity of Function 52 2.6 Exercise 54 Chapter 3 Characteristics of Linear Programming 57 3 Poles 6 1 3.2 Simplex Algorithm 64 3.2./ Kloc-0/ Basic Principle 2 Algorithm Steps and Simplex Table 67 3.2.3 Starting Mechanism 70 3.3 Optimality Conditions of Linear Programming 77 3.4 Dual Theory 79 3.4. 1 Dual Theorem 79 3.4.2 Improvement and Extension of Dual Simplex Method 84 3.5 Simplex Method 88 3.5. 1 Modified simplex method 88 3.5.2 primitive 5.5 concept 108 3.6.2 simplex algorithm complexity 65438+ .3 Karmarkar projection scale algorithm 1 14 3.6.4 primitive-dual scale algorithm1243. Optimality conditions for 438+0 unconstrained optimization 150 4.2 algorithm convergence 152 4.2 one-dimensional search and convergence 152 4.2 algorithm mapping and convergence 162 4.2.3 convergence speed and algorithm stopping rules 1 664.438. 70 4.3.2 Local Convergence 172 4.3.3 Modified Newton Method 174 4.3.4 Inexact Newton Method 177 4.4 * * Yoke Direction and Linearity * * * Yoke Gradient Method 179 Yoke Direction and Extended Subspace Theorem/. Kloc-0/8655 Yoke Gradient Method 192 4.6 Quasi-Newton Method 196 4.6. 1 Quasi-Newton Condition and Algorithm Steps 196 4.6.2 Symmetric Rank 1 Modified Formula197. Constrained optimization 220 5. 1 First-order optimality condition and constraint specification 220 5. 1.2 First-order necessary condition 220 5. 1.2 constraint specification 226 5. 1.3 First-order sufficient condition 228 5.2 Second-order optimality condition 230 5.2./klc Second-order.2 Second-order Sufficient Condition 233 5.3 Duality Theory 235 5.3. 1 Feasible Direction Method 265 5.5. 1 Zoutendijk feasible direction method 266 5.5.2 Rosen gradient projection method 268 5.5.3 Wolfe reduced gradient method 270 5.5.4 Frank-Wolfe linearization method 272 5.6 sequence unconstrained method 273 5.6.65438+ sub-penalty function method 275 5.6.2 logarithmic obstacle function method 280 5.6.3 multiplier method. Sub-programming Method 288 Direction Finding Decline 299 5.8 Trust Region Method 305 5.8. 1 Basic Principle of Trust Region Method 305 5.8.2 Exact Solution of Subproblem 308 5.8.3 Approximate Solution of Subproblem 3 13 5.8.4 Global Convergence of Trust Region Method 3 1 8 5.9 Exercise 365438+ 438+0 Introduction 325 6.2 Efficient Points and Weak Efficient Points of Vector Set 327 6 and G- Efficient Solution 335 6 Solution of Multi-objective Programming 338 6.4. 1 Method Based on a Single Objective Problem 339 6.4.2 Method Based on Multiple Single Objective Problems 343 6.5 Exercise 345 Chapter 7 Combinatorial Optimization and Integer Programming 347 7. Kloc-0/ Network Flow Problems and Algorithms 348 7. 1 Basic concepts in graph theory348 7.65544566.5436.5437.5436.46.536.46.47.537.46.46.47.47.47.565.567.567.5 Quality 362 7.3./ Model of Integer Programming 363 7.3.2 Properties of Integer Programming 366 7.4 Cutting Plane Method 37 1 7.4. 1 Gomory Cutting Plane Method 37 1 7.4.2 Method of Constructing Effective Inequalities 379 7.5 Branch and Bound Method 381740/Kloc Properties of kloc-0/ convex set 40/continuity and concavity of kloc-0/.2 function 403 8. 1.3 convex envelope 405 8. 1.4 Lipschitz function 409 8. 1.5 d. 8.2 Common global optimization model 4/kloc-. 3 8.2.6 Principle 427 8.3.2 Cutting Plane Algorithm 429 8.3.3 Method for Solving Relaxation Problems 43 1 8.4 Concave Cutting Method 433 8.4. 1 Effective Cutting and Concave Cutting 434 8.4.2 Convergence of Concave Cutting Method 437 8.4.3 Concave Cutting with Anti-Convex Constraints 4378.4.3.