Nonlinear programming problems are to minimize general nonlinear functions, possibly subject to some nonlinear constraints. In this paper, we review some recent results on nonlinear optimization.
This paper studies the three-term conjugate gradient method for unconstrained optimization. The method includes the classical (two-term) conjugate gradient method and the famous Beale-Powell restart algorithm as its s...This paper studies the three-term conjugate gradient method for unconstrained optimization. The method includes the classical (two-term) conjugate gradient method and the famous Beale-Powell restart algorithm as its special forms. Some mild conditions are given in this paper, which ensure the global convergence of general three-term conjugate gradient methods.展开更多
SLMQN is a subspace limited memory quasi-Newton algorithm for solving largescale bound constrained nonlinear programming problems. The algorithm is suitable to these large problems in which the Hessian matrix is diffi...SLMQN is a subspace limited memory quasi-Newton algorithm for solving largescale bound constrained nonlinear programming problems. The algorithm is suitable to these large problems in which the Hessian matrix is difficult to compute or is dense,or the number of variables is too large to store and compute an n x n matris. Due to less storage requirement, this algorithm can be used in PCs for solving medium-sized and large problems. The algorithm is implemented in Fortran 77.展开更多
基金The author is supported by a grant from the Academia Sinica
文摘Nonlinear programming problems are to minimize general nonlinear functions, possibly subject to some nonlinear constraints. In this paper, we review some recent results on nonlinear optimization.
文摘This paper studies the three-term conjugate gradient method for unconstrained optimization. The method includes the classical (two-term) conjugate gradient method and the famous Beale-Powell restart algorithm as its special forms. Some mild conditions are given in this paper, which ensure the global convergence of general three-term conjugate gradient methods.
文摘SLMQN is a subspace limited memory quasi-Newton algorithm for solving largescale bound constrained nonlinear programming problems. The algorithm is suitable to these large problems in which the Hessian matrix is difficult to compute or is dense,or the number of variables is too large to store and compute an n x n matris. Due to less storage requirement, this algorithm can be used in PCs for solving medium-sized and large problems. The algorithm is implemented in Fortran 77.
