In maximizing a non-linear function G(0), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1-1 transformation on the variables 0, so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse tr...

In this paper, the methods for use of prior information about multiple operating environments, in improving adaptive filter convergence properties are discussed. More concretely, the gain selection, profiling and scheduling in steepest descent algorithms are treated in detail. Work presented in this paper is an extension of [1]. Two flavors of optimization are discussed: average descent rate op...

GANs excel at learning high dimensional distributions, but they can update generator parameters in directions that do not correspond to the steepest descent direction of the objective. Prominent examples of problematic update directions include those used in both Goodfellow’s original GAN and the WGAN-GP. To formally describe an optimal update direction, we introduce a theoretical framework whi...

The satissability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design eecient optimization algorithms for nding a solution for a satissable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed 31, 35, 34, ...