This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions...

In this paper we address the question of how many objective functions are really needed to decide whether a given point is Pareto optimal. We prove a reduction result for the case of quasi-convex objective functions and a convex feasible set. This result states that in order to decide whether a point x in the decision space is Pareto optimal it suuces to consider at most n + 1 objectives at a t...

This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both l...

We consider the problem of optimally acquiring and retiring assets that are undergoing technological change over an unbounded horizon. The allowance for technological change prevents one from adopting the classic repeated-plant assumption that future replacements will be identical in costs to current asset contenders, thus confronting one with a non-stationary infinite horizon problem to solve....

We present a multiagent learning approach to satisfy any given optimality criterion in repeated game self-play. Our approach is opposed to classical learning approaches for repeated games: namely, learning of equilibrium, Paretoefficient learning, and their variants. The comparison is given from a practical (or engineering) standpoint, i.e., from a point of view of a multiagent system designer ...

The selection problem of an optimal set sensors estimating the snapshot high-dimensional data is considered. objective functions based on various criteria design are adopted to greedy method: D-optimality, A-optimality, and E-optimality, which maximizes determinant, minimize trace inverse, maximize minimum eigenvalue Fisher information matrix, respectively. First, matrix derived depending numbe...

We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimat...

This paper deals with denumerable-state continuous-time controlled Markov chains with possibly unbounded transition and reward rates. It concerns optimality criteria that improve the usual expected average reward criterion. First, we show the existence of average reward optimal policies with minimal average variance. Then we compare the variance minimization criterion with overtaking optimality...