Displaying similar documents to “Two dimensional optimal transportation problem for a distance cost with a convex constraint”

Regularity properties of optimal transportation problems arising in hedonic pricing models

Brendan Pass (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form () = ( + ) where is a convex function on ℝ. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely...

Optimal Policies for a Database System with Two Backup Schemes

Cunhua Qian, Yu Pan, Toshio Nakagawa (2010)

RAIRO - Operations Research

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This paper considers two backup schemes for a database system: a database is updated at a nonhomogeneous Poisson process and an amount of updated files accumulates additively. To ensure the safety of data, full backups are performed at time or when the total updated files have exceeded a threshold level , and between them, cumulative backups as one of incremental backups are made at periodic times ). Using the theory of cumulative processes, the expected cost is...

Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is  = d  + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the...

An Extended Opportunity-Based Age Replacement Policy

Bermawi P. Iskandar, Hiroaki Sandoh (2010)

RAIRO - Operations Research

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The present study proposes an extended opportunity-based age replacement policy where opportunities occur according to a Poisson process. When the age, of the system satisfies for a prespecified value , a corrective replacement is conducted if the objective system fails. In case satisfies for another prespecified value , we take an opportunity to preventively replace the system by a new one with probability , and do not take the opportunity with probability . At the moment reaches...

On convex sets that minimize the average distance

Antoine Lemenant, Edoardo Mainini (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study the compact and convex sets K ⊆ Ω ⊆ ℝ2that minimize ∫ Ω ( , K ) d + λ 1 Vol ( K ) + λ 2 Per ( K ) ∫ Ω dist ( x ,K ) d x + λ 1 Vol ( K ) + λ 2 Per ( K ) for some constantsλ 1 and λ 2, that could possibly be zero. We compute in particular the second order derivative of the functional and use...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

ESAIM: Probability and Statistics

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The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function :  ×  →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.

An Improved Algorithm for a Bicriteria Batching Scheduling Problem

Cheng He, Xiumei Wang, Yixun Lin, Yundong Mu (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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This note is concerned with the bicriteria scheduling problem on a series-batching machine to minimize maximum cost and makespan. An ( ) algorithm has been established previously. Here is an improved algorithm which solves the problem in ( ) time.

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

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Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal....

Global optimality conditions for a dynamic blocking problem

Alberto Bressan, Tao Wang (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper is concerned with a class of optimal blocking problems in the plane. We consider a time dependent set () ⊂ ℝ, described as the reachable set for a differential inclusion. To restrict its growth, a barrier can be constructed, in real time. This is a one-dimensional rectifiable set which blocks the trajectories of the differential inclusion. In this paper we introduce a definition of “regular strategy”, based on a careful classification of blocking arcs. Moreover, we derive...