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Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities

Lulu Yin, Hongwei Liu, Jun Yang (2022)

Applications of Mathematics

We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence rate...

Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case

Nico M. van Dijk, Karel Sladký (2006)

Kybernetika

This second Part II, which follows a first Part I for the discrete-time case (see [DijkSl1]), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions,...

Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case

Nico M. van Dijk, Karel Sladký (2006)

Kybernetika

In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as generalization of the pure stochastic case, for arbitrary dynamic systems governed by nonnegative matrices. Part I covers the discrete-time and Part II the continuous-time case. The research has initially been motivated by a reliability application contained in Part II. In the present Part I it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly...

More on the tournament equilibrium set

G. Laffond, J. F. Laslier, M. Le Breton (1993)

Mathématiques et Sciences Humaines

Schwartz (1990) proposed a new solution concept for choosing from a tournament ; called the Tournament Equilibrium Set. He stated four problems concerning this solution. In this paper we introduce further questions and demonstrate some logical relationship between these questions.

Multi-attribute evaluation with imprecise vector utility

Sixto Ríos-Insua, Alfonso Mateos (1996)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

We consider the multi-attribute decision making problem with incomplete information on the decision maker's preferences, given by an imprecise vector utility function. We introduce an approximation set to the utility efficient set which may be used to aid a decision maker in reaching a final compromise strategy. We provide sorne properties and an interactive procedure based on such approximation set.

Multistage risk premiums in portfolio optimization

Miloš Kopa, Barbora Petrová (2017)

Kybernetika

This paper deals with a multistage stochastic programming portfolio selection problem with a new type of risk premium constraints. These risk premiums are constructed on the multistage scenario tree. Two ways of the construction are introduced and compared. The risk premiums are incorporated in the multistage stochastic programming portfolio selection problem. The problem maximizes the multivariate (multiperiod) utility function under condition that the multistage risk premiums are smaller than...

Multivariate stochastic dominance for multivariate normal distribution

Barbora Petrová (2018)

Kybernetika

Stochastic dominance is widely used in comparing two risks represented by random variables or random vectors. There are general approaches, based on knowledge of distributions, which are dedicated to identify stochastic dominance. These methods can be often simplified for specific distribution. This is the case of univariate normal distribution, for which the stochastic dominance rules have a very simple form. It is however not straightforward if these rules are also valid for multivariate normal...

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