In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlinear equality and inequality constraints. Comparing with other methods for these problems, the algorithm...In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlinear equality and inequality constraints. Comparing with other methods for these problems, the algorithm has two main advantages. First, it doesn’t solve any quadratic programming (QP), and its search directions are determined by the generalized projection technique and the solutions of two systems of linear equations. Second, the sequential points generated by the algorithm satisfy all inequality constraints and its step length is computed by the straight line search. The algorithm is proved to possess global and superlinear convergence.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In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlinear equality and inequality constraints. Comparing with other methods for these problems, the algorithm has two main advantages. First, it doesn’t solve any quadratic programming (QP), and its search directions are determined by the generalized projection technique and the solutions of two systems of linear equations. Second, the sequential points generated by the algorithm satisfy all inequality constraints and its step length is computed by the straight line search. The algorithm is proved to possess global and superlinear convergence.
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.
