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Economic equilibrium through variational inequalities

Magdalena Nockowska-Rosiak (2009)

Applicationes Mathematicae

The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...

Empirical regression quantile processes

Jana Jurečková, Jan Picek, Martin Schindler (2020)

Applications of Mathematics

We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of various types in the situations with covariates.

Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Pedro Merino, Fredi Tröltzsch, Boris Vexler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.

Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

Eduardo Casas (2002)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L ∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states....

Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints

Eduardo Casas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states. ...

Estudio computacional de algunos nuevos algoritmos heurísticos para el problema de planificación de proyectos con limitación de recursos.

Ramón Alvarez-Olaguibel, José Manuel Tamarit Goerlich, Vicente Valls Verdejo (1988)

Trabajos de Investigación Operativa

El trabajo describe dos métodos de diseño de algoritmos heurísticos para el problema de planificación de un proyecto con limitación de recursos. El primer método es constructivo: las actividades del proyecto se intentan incorporar a la secuencia posible tan pronto como lo permiten sus relaciones de precedencia, resolviendo de diversas formas los conflictos provocados por la limitación de recursos. El segundo enfoque está basado en la idea de incorporar arcos disjuntos para resolver las incompatibilidades...

Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems

Xue-Fang Wang, Zhenhua Deng, Song Ma, Xian Du (2017)

Kybernetika

In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed...

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