1. Constrained optimization methods include feasible directions, projection, interior point, and Lagrange multiplier methods.

2. In convex programming theory, a constrained optimization problem, by KT conditions, is usually converted into a mixed nonlinear complementarity problem.

3. A constrained optimization problem in primal weight space with incorporation of a regularization term was discussed. The dual problem was solved by using the kernel trick.

4. Santos ( 1998 ) and the region algorithm is usedtogether for solving the equality constrained optimization.

5. Chapter 3 constructs a new generalized pattern search method for linear equality constrained optimization problems and gives the proofs of the global convergence.

6. This paper gives a feasible trust - region dogleg path algorithm for solving nonlinear inequality constrained optimization problems.

7. Formative approximation problem is solved by variable metric method for constrained optimization.

8. Sequential Unconstrained Minimization Techniques (SUMT) are most common and comparatively successful method in constrained optimization.

9. In this paper, we give three convergence algorithm models for nonlinearly constrained optimization problems.

10. In the third chapter, nonmonotonic trust region algorithms for nonlinear constrained optimization are discussed.

11. So, the calculation of normal depth problem was converted into a nonlinear constrained optimization problem, which can be solved by the pattern search optimization method.

12. In the second chapter, nonmonotonic trust region algorithms for linear constrained optimization are discussed.

13. In the paper, a varied step length LMS algorithm is adopted in space-time multiuser receiver, in which a new bierror function is used to solve the constrained optimization problem.