We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the s...

We consider a linear algebraic system A(p)x = b(q), where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters varying within given intervals. The linear tolerance problem for the so-called parametric tolerable solution set Σtol(A(p), b(q), [p], [q]) = {x ∈ Rn | (∀p ∈ [p])(∃q ∈ [q])(A(p)x = b(q))} requires an inner estimation of this solution se...

We present a case study of a difficult real-world pattern recognition problem: predicting hard drive failure using attributes monitored internally by individual drives. We compare the performance of support vector machines (SVMs), unsupervised clustering, and non-parametric statistical tests (rank-sum and reverse arrangements). Somewhat surprisingly, the rank-sum method outperformed the other m...

Abstract We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted lot of interest in recent years. However, so far, scalarization has appeared to be the main approach used deal problem. Here, we utilize concept frontier map that extends notion optimal value function our parametric Based on this, build t...

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

For finding zeros or fixed points of set-valued maps, the fact that the space of convex, compact, nonempty sets of R is not a vector space presents a major disadvantage. Therefore, fixed point iterations or variants of Newton’s method, in which the derivative is applied only to a smooth single-valued part of the set-valued map, are often applied for calculations. We will embed the set-valued ma...

Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...

A stabilization problem for a general nonlinear control system is considered. In particular the control corresponding to the equilibrium position may belong to the boundary of the control set. A linear control system is considered as a first approximation for the original problem. The right-hand side of the linear system generates a set-valued map of a special type known as a convex process. Th...

We consider the problem of reinforcement learning in a controlled Markov environment with multiple objective functions of the long-term average reward type. The environment is initially unknown, and furthermore may be affected by the actions of other agents, actions that are observed but cannot be predicted beforehand. We capture this situation using a stochastic game model, where the learning ...

In this paper, we establish some sufficient conditions for the existence of a solution equilibrium problem. The problem is understood in general form: find $ \overline{x}\in E such that$ \begin{equation*} \Phi(\overline{x},y) \vartriangleleft (-D\backslash\{0\})^c \text{ all }y \in E; \end{equation*} $and its variants, where Boolean-valued bifunction and \Phi multivalued mapping with values vec...