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A new criterion is introduced for comparing the convergence properties of variable metric algorithms, focusing on stepwise descent properties. This criterion is a bound on the rate of decrease in the function value at each iterative step (single-step convergence rate). Using this criterion as a basis for algorithm development leads to the introduction of variable coefficients to rescale the objective function at each iteration, and, correspondingly, to a new class of variable metric algorithms. Effective sealing can be implemented by restricting the parameters in a two-parameter family of variable metric algorithms. Conditions are derived for these parameters that guarantee monotonic improvement in the single-step convergence rare. These conditions are obtained by analyzing the eigenvalue structure of the associated inverse Hessian approximations. [ABSTRACT FROM AUTHOR]

A dynamic decision problem in which the effect of control action is either delayed for a number of time periods or has an effect that lasts for a fixed period leads, in the conventional formulation, to a high-dimensional dynamic-programming problem. This paper develops a method for exploiting the inherent structure of such problems that leads to low-dimensional 'cyclic dynamic programming' problems that are easier to solve than the problem that is obtained by the conventional approach. [ABSTRACT FROM AUTHOR]

This paper presents a decomposition procedure for extending the size of problems that can be solved using dynamic programming. It essentially consists of decomposing the tabular arrays of data into blocks of data, and then performing the dynamic programming calculations over the whole tabular array by calculating on each block separately. [ABSTRACT FROM AUTHOR]