解约束优化问题的SQP(Sequential Quadratic Programming)方法探讨

Discussion on SQP (Qequential QuadraticProgramming) Method for SolvingConstraint Optimization Problems

摘要: 本文详细介绍SQP (sequential quadratic programming)方法的设计过程与具体算法，并通过解决等式约束优化问题和不等式约束优化问题的例子来讨论其优劣性，探讨它的扩展性。SOP算法的设计核心是将原来一般约束问题的解转换为一系列简单子问题(例如二次规划问题)的求解。而二次规划问题的求解方法非常成熟与完善，这种将复杂优化问题的求解转化一系列简单问题的求解方法被提出之后广受欢迎，使得SQP方法成为解决非线性约束优化最有效的方法之一。它在解决具有非线性优化问题时有它独特的优势。理解和掌握它，对于理解与应用其它的SOP方法也有极大的帮助。

Abstract: This paper introduces the design process and specific algorithm of SQP (sequential quadratic programming) in detail, and discusses its advantages and disadvantages and its expansibility by solving an example of equality constraint optimization problem and inequality constraint optimization problem. The core of SQP algorithm is to convert the original solution of general constraint problem into a series of simple subproblems (such as quadratic programming problem). However, the solution method of quadratic programming problem is very mature and perfect. This method, which transforms the solution of complex optimization problems into a series of simple problems, has been widely popular after being proposed, making SQP method one of the most effective methods to solve nonlinear constrained optimization. It has its unique advantages in solving nonlinear optimization problems. Understanding and mastering it is also of great help to understand and apply other SQP methods.