In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and dualit...In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.展开更多
A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any...A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（60574075） University, engaged in optimization theory and application.
文摘In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.
基金supported by the National Science Foundation of USA(Grant Nos.1522629 and 1522654)the Office of Naval Research of USA(Grant Nos.N00014-11-1-0068 and N00014-15-12048)+1 种基金the Air Force Research Laboratory of USA(Contract No.FA8651-08-D-0108/0054)National Natural Science Foundation of China(Grant No.11571178)
文摘A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.
