理解運籌學中二次規劃與投資組合

• 二次規劃（Quadratic programming）

  二次規劃，是運籌學中一種特殊類型的最優化問題。

• Quadratic programming(QP)

  Quadratic programming is the process of solving a special type of mathematical opetimization problem - sepcially, a (linearly constrained) quadratic optimization problem, that is the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.

  Quadratic programming is a particular type of nonlinear programming.

  quadratic function

  In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables(項) in which the highest-degree（次） term is of the second degree.

  二次函數，可能是二次單變量函數，也可能是二次多項式函數。

  The objective function can contain bilinear or up to second order polynomial terms, and the constraints are linear and can be both equalities and inequalities.

• References

1. wikipedia : quadratic programming
2. Northwestern University Chemical Process Design Open Textbook : Quadratic programming
3. Optimization Theory : Chapter 3