Generalized Geometric Programming Problem Several Algorithms

In this thesis, we study the generalized geometric programming problems. There are three algorithms proposed to solve the problems. Firstly, a new modified Crout factorization of forcing real symmetric tridiagonal matrixes to be positive definite is given, base which, we present a nonmonotone improved Newton method for the unconstrained geometric programming problems. Secondly, we give a LMGQT trust region method with line search trick by combining the step length of trust region for the unconstrained geometric programming problems. Finally, we weaken the Mangasar-ian conditions for general constrained optimization problems, and propose a class of more generalized Lagrange functions. Then the problems with mixed constraints can be converted to nonlinear equation, and we give an algorithm for the generalize geometric programming problems with mixed constraints. We prove respectively that the algorithms are convergent, and the numerical experiments validate our conclusions of our methods.