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  锥优化的基于核函...
  ￥30.02元

　　本书对一种新的内点算法——基于核函数的原始对偶内点算法以及算法的复杂性进行了系统的介绍。首先对锥优化，包括线性规划、二阶锥优化、半正定优化的对偶理论,　最优性条件、中心路径进行详细的介绍；其次介绍解线性规划、二阶锥优化和半正定优化的基于核函数的内点算法以及复杂性分析。同时本书也介绍锥优化问题内点算法研究的最新研究进展。
　　全书共分十章:第一章为引言。第二章到第四章介绍锥规划的对偶理论，最优性条件，中心路径。第五章介绍核函数以及对应的罚函数的性质。第六章至第九章分别叙述线性规划问题，非线性互补问题，半正定规划问题，二阶锥优化问题的基于新核函数的原始－对偶内点算法。第十章介绍内点算法在结构优化设计中的应用。

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• Preface
  Chapter 1 Introduction
  1.1 Conic optimization problems
  1.2 Conic duality
  1.3 From the dual cone to the dual problem
  1.4 Development of the interior-point methods
  1.5 Scope of the book
  Chapter 2 Kernel Functions
  2.1 Definition of kernel functions and basic properties
  2.2 The further conditions of kernel functions
  2.3 Properties of kernel functions
  2.4 Examples of kernel functions
  2.5 Barrier functions based on kernel functions
  2.6 Generalization of kernel function
  2.6.1 Finite kernel function
  2.6.2 Parametric kernel function
  Chapter 3 Kernel Function-based Interior-point Algorithm for LO
  3.1 The central path for LO
  3.2 The search directions for LO
  3.3 The generic primal-dual interior-point algorithm for LO
  3.4 Analysis of the algorithm
  3.4.1 Decrease of the barrier function during an inner iteration
  3.4.2 Choice of the step size
  3.5 Iteration bounds
  3.6 Summary of computation for complexity bound
  3.7 Complexity analysis based on kernel functions
  3.8 Summary of results
  Chapter 4 Kernel Function-based Interior-point Algorithm forP*(κ) LCP
  4.1 The P_*(κ)-LCP
  4.2 The central path for P_*(κ)-LCP
  4.3 The new search directions for P_*(κ)-LCP
  4.4 The generic primal-dual interior-point algorithm for P_*(κ)-LCP
  4.5 The properties of the barrier function
  4.6 Analysis of the algorithm
  4.6.1 Growth behavior of the barrier function
  4.6.2 Determining the default step size
  4.7 Decrease of the barrier function during an inner iteration
  4.8 Complexity of the algorithm
  4.8.1 Iteration bound for the large-update methods
  4.8.2 Iteration bound for the small-update methods
  Chapter 5 Kernel Function-based Interior-point Algorithm for SDO
  5.1 Special matrix functions
  5.2 The central path for SDO
  5.3 The new search directions for SDO
  5.4 The generic primal-dual interior-point algorithm for SDO
  5.5 The properties of the barrier function
  5.6 Analysis of the algorithm
  5.6.1 Decrease of the barrier function during an inner iteration
  5.6.2 Choice of the step size
  5.7 Iteration bounds
  5.8 Kernel function-based schemes
  5.9 The example
  5.10 Numerical results
  Chapter 6 Kernel Function-based Interior-point Algorithm for SOCO
  6.1 Algebraic properties of second-order cones
  6.2 Barrier functions defined on second-order cone
  6.3 Rescaling the cone
  6.4 The central path for SOCO
  6.5 The new search directions for SOCO
  6.6 The generic primal-dual interior-point algorithm for SOCO
  6.7 Analysis of the algorithm
  6.8 The crucial inequality
  6.9 Decrease of the barrier function during an inner iteration
  6.10 Increase of the barrier function during a u-update
  6.11 Iteration-bounds
  6.12 Numerical results
  6.13 Some technical lemmas
  Appendix Three Technical Lemmas
  Reference