We propose an Economic Probabilistic analogy: the category of cost is analogous to the category of Probability. The proposed analogy permits construction of an informal theory of nonlinear non-convex Gaussian Utility and Cost, which describes the real economic processes more adequately than a theory based on a linear and convex models. Based on the proposed analogy, we build a nonlinear non-con...

In this paper, we generalize the λ test. The generalized λ test can be applied towards determining whether there exist data dependences for coupled arrays with both constant and variable limits under any given direction vectors, improving the applicable range of the λ test. Experimental data reflecting the effect of the generalized λ test are also presented.

Conventional measures of model fit for indexed data (e.g., time series or spatial data) summarize errors in y, for instance by integrating (or summing) the squared difference between predicted and measured values over a range of x. We propose an approach which recognizes that errors can occur in the x-direction as well. Instead of just measuring the difference between the predictions and observ...

In this paper we explore the relations between the standard dual problem of a convex generalized fractional programming problem and the “partial” dual problem proposed by Barros et al. (1994). Taking into account the similarities between these dual problems and using basic duality results we propose a new algorithm to directly solve the standard dual of a convex generalized fractional programmi...

This paper considers a computational approach to obtain a reduced order model for polynomial nonlinear systems. The approach is based on balancing generalized gramians of polynomial systems and truncating the systems based on the balanced generalized gramians. The approach utilizes sum of squares programming for its computational purposes.

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir type vector duals.

Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...

A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to be affected by norm-bounded disturbance and to have both norm-bounded uncertainties in the realization matrices as well as nonlinear model uncertainties. W...