It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general...It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general semide finite programming even if both the primal problem and its dual problem are strictly feasible. Some other properties are also concerned.展开更多
Levenb erg-M arquardt method was first suggested by Levenberg and Marquardt in the context of nonlinear least sqares. This paper will develop a Levenberg-Marquardt method for semidefinite programming, which is global ...Levenb erg-M arquardt method was first suggested by Levenberg and Marquardt in the context of nonlinear least sqares. This paper will develop a Levenberg-Marquardt method for semidefinite programming, which is global collvergence and easy to implement. Some promising numerical results are also contained.展开更多
In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear...In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear independent assumption on the gradients of the equalitiy constraints, we prove the global convergence results for the main algorithm and indicate that they extend the results on SQP and those on trust region methods for equality constrained optimizstion and for optimization with simple bounds. Moreover, since any nonlinear programming problem can be converted into the standard nonlinear programming by introducing slack variables, the trust region method preseated in this paper can be used for solving general nonlinear programming problems.展开更多
文摘It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general semide finite programming even if both the primal problem and its dual problem are strictly feasible. Some other properties are also concerned.
文摘Levenb erg-M arquardt method was first suggested by Levenberg and Marquardt in the context of nonlinear least sqares. This paper will develop a Levenberg-Marquardt method for semidefinite programming, which is global collvergence and easy to implement. Some promising numerical results are also contained.
文摘In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear independent assumption on the gradients of the equalitiy constraints, we prove the global convergence results for the main algorithm and indicate that they extend the results on SQP and those on trust region methods for equality constrained optimizstion and for optimization with simple bounds. Moreover, since any nonlinear programming problem can be converted into the standard nonlinear programming by introducing slack variables, the trust region method preseated in this paper can be used for solving general nonlinear programming problems.
