Sqp Algorithm In The Nonlinear Constraints

This thesis solves nonlinear optimization using SQP method. In the first chapter, introduces a new SQP algorithm for nonlinear optimization with equality and inequality constraint. We need only solving one quadratic sub-problem at each iteration and modify the feasible direction and automatically in order to avoid the Marotos effect. The method could retain the global convergence under the weak condition. In the second chapter, a feasible sequential equality constrained quadratic programming algorithm is proposed to solve the nonlinear inequality constrained optimization. Per single iteration, it is only necessary to solve three equality constrained quadratic programmings with the same scale. So the computational effort is reduced. In the third chapter, introduces a new algorithm for nonlinear optimization which applies filter techniques to the traditional line search penalty function method. Unlike formal filter methods, do not need restoration phase here. And under reasonable assumptions, global convergence is given.