One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set.The present work is concerned with the co...

– The standard multiple criteria optimization starts with an assumption that the criteria are incomparable. However, there are many applications in which the criteria express ideas of allocation of resources meant to achieve some equitable distribution. This paper focuses on solving linear multiple criteria optimization problems with uniform criteria treated in an equitable way. An axiomatic de...

Decentralized optimization of distributed stochastic differential systems has been an active area of research for over half a century. Its formulation utilizing static team and person-by-person optimality criteria is well investigated. However, the results have not been generalized to nonlinear distributed stochastic differential systems possibly due to technical difficulties inherent with dece...

Among optimality criteria adopted to select best experimental designs to discriminate between different models, the KL-optimality criterion is very general. A KL-optimum design is obtained from a minimax optimization problem on an infinite-dimensional space. In this paper some important properties of the KL-optimality criterion function are highlighted and an algorithm to construct a KL-optimum...

To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of estimator from a general subsampling algorithm are established, optimal probabilities A- L-optimality criteria derived. Furthermore, using Frobenius norm matrix conce...

We provide an optimality criteria for a perfect matching with respect to the Clar problem in 2-connected plane bipartite graphs.

Abstract. This contribution is devoted to the risk-sensitive optimality criteria in finite state Markov Decision Processes. At first, we rederive necessary and sufficient conditions for average optimality of (classical) risk-neutral unichain models. This approach is then extended to the risk-sensitive case, i.e., when expectation of the stream of one-stage costs (or rewards) generated by a Mark...

A metapopulation consists of interacting populations, each occupying distinct spatially separated patches of habitat. Modelling these populations has become increasingly important because anthropogenic impacts on spatially homogeneous populations have led to increased habitat fragmentation and accidental introduction of invasive species. We employ a two-parameter continuous-time Markovian model...

Ž . The study of expectation optimality criteria standard criteria has constituted most previous work in the area of Markov decision processes Ž . MDPs . However, the optimal policies obtained from such models are not reliable when considering a single or a few decision processes, since only the average performance over many trials is guaranteed to be optimal. In fact, the expectation optimalit...

In this chapter we study Markov decision processes (MDPs) with nite state and action spaces. This is the classical theory developed since the end of the fties. We consider nite and in nite horizon models. For the nite horizon model the utility function of the total expected reward is commonly used. For the in nite horizon the utility function is less obvious. We consider several criteria: total...