Mathematical optimization数学上的最优化

https://en.wikipedia.org/wiki/Mathematical_optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

在数学、计算机科学和运筹学中，数学优化或数学规划，或者拼写优化，是从一组备用的方案中选出最佳元素（参考某些标准）。

In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.

在最简单的情况下，一个优化问题包括通过在一个允许集合内系统地选择输入值和计算函数的值来最大化或最小化实函数。最优化理论和技术对其他公式的推广构成了应用数学的一个大领域。更一般地，优化包括找到给定定义域（或输入）的一些目标函数的“最佳可用”值，包括各种不同类型的目标函数和不同类型的域。

Contents

• 1Optimization problems
• 2Notation
  • 2.1Minimum and maximum value of a function
  • 2.2Optimal input arguments
• 3History
• 4Major subfields
  • 4.1Multi-objective optimization
  • 4.2Multi-modal optimization
• 5Classification of critical points and extrema
  • 5.1Feasibility problem
  • 5.2Existence
  • 5.3Necessary conditions for optimality
  • 5.4Sufficient conditions for optimality
  • 5.5Sensitivity and continuity of optima
  • 5.6Calculus of optimization
• 6Computational optimization techniques
  • 6.1Optimization algorithms
  • 6.2Iterative methods
  • 6.3Global convergence
  • 6.4Heuristics
• 7Applications
  • 7.1Mechanics
  • 7.2Economics and finance
  • 7.3Electrical engineering
  • 7.4Civil engineering
  • 7.5Operations research
  • 7.6Control engineering
  • 7.7Geophysics
  • 7.8Molecular modeling
• 8Solvers
• 9See also
• 10Notes
• 11Further reading
  • 11.1Comprehensive
    • 11.1.1Undergraduate level
    • 11.1.2Graduate level
  • 11.2Continuous optimization
  • 11.3Combinatorial optimization
  • 11.4Relaxation (extension method)
• 12Journals
• 13External links