Search

A new subspace minimization conjugate gradient algorithm with a nonmonotone Wolfe line search is proposed and analyzed. In the scheme, we propose two choices of the search direction by minimizing a quadratic approximation of the objective function in special subspaces, and state criterions on how to choose the direction. Under given conditions, we obtain the significant conclusion that each choice of the direction satisfies the sufficient descent property. Based on the idea on how the function is close to a quadratic function, a new strategy for choosing the initial stepsize is presented for the line search. With the used nonmonotone Wolfe line search, we prove the global convergence of the proposed method for general nonlinear functions under mild assumptions. Numerical comparisons are given with well-known CGOPT and CG_DESCENT and show that the proposed algorithm is very promising. [ABSTRACT FROM AUTHOR]

The paper presents a numerical procedure for dynamic analysis of box girders with tee-stiffeners utilizing unconstrained optimization techniques. Unlike the finite element or finite strip methods, the procedure does not require discretization to the whole structure, thus resulting in great savings in computational time. The potential and kinetic energy of the assembled structure is expressed in terms generalized functions that describe the longitudinal and transverse displacement profiles. The problem is then converted into uunconstrained optimization problem to determine the magnitude of the lowest natural frequency and the associated mode shape. Results are presented showing the sensitivity the natural frequency to the stiffener depth (d) and the flange width (b). It is shown that the number of longitudinal and transverse stiffeners largely influence the magnitude of the natural frequency (λ) of the box girder. Design guidelines are also provided to optimize the dynamic response of the structure. The procedure is very practical and can be utilized in the industry for the analysis of box girders. [ABSTRACT FROM AUTHOR]

This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented. [ABSTRACT FROM AUTHOR]