Dynamic Walrasian price equilibrium problem: evolutionary variational approach with sensitivity analysis

Donato, Maria Bernadette; Milasi, Monica; Vitanza, Carmela

doi:10.1007/s11590-007-0047-4

Cited by 19 publications

(13 citation statements)

References 12 publications

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“…We now prove that the pollution control equilibrium vector satisfying conditions (8)- (11) is also a solution to variational inequality problem (13).…”

Section: T))dt Is Fréchet Differentiable For All I With Respect To (Ementioning

confidence: 91%

“…In this section we prove that the optimal solution of problem (6) is also a solution to an evolutionary variational inequality problem, which in turn is equivalent to equilibrium conditions (8)- (11).…”

Section: The Variational Inequality Formulationmentioning

confidence: 98%

“…In addition, we attempt to refine models in the literature, taking into account the evolution of the system with respect to time, and hence assuming that all data are time-specific. It is indeed well-recognized (see for instance [2,8,11,14,22,23,[29][30][31][32][33]) the importance of studying dynamic problems in order to represent model adjustment processes and equilibrium with lags. The mathematical framework chosen for the study of the model is that of infinite dimensional variational inequalities (see the fundamental manuscripts [17,34] and the books [9,15,21] for both theory and applications on finite and infinite dimensional variational inequalities).…”

Section: Introductionmentioning

confidence: 99%

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A variational inequality formulation of the environmental pollution control problem

Scrimali

2009

Optim Lett

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In this paper we develop the time-dependent pollution control problem in which different countries aim to determine the optimal investment allocation in environmental projects and the tolerable pollutant emissions, so as to maximize their welfare. We provide the equilibrium conditions governing the model and derive the evolutionary variational inequality formulation. The existence of solutions is investigated and a numerical example is also presented.

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“…We now prove that the pollution control equilibrium vector satisfying conditions (8)- (11) is also a solution to variational inequality problem (13).…”

Section: T))dt Is Fréchet Differentiable For All I With Respect To (Ementioning

confidence: 91%

Section: The Variational Inequality Formulationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A variational inequality formulation of the environmental pollution control problem

Scrimali

2009

Optim Lett

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show abstract

“…It is by now recognized the importance and the necessity of studying evolutionary problems, in order to represent reliable models, that take into account equilibria adjustment processes or retarded equilibria (see, for instance, [19][20][21][22][23][24][25][26][27][28][29][30][31]). In fact, the static approach that is a first important step for modeling real phenomena, describes systems that naturally evolve in time, only in a fixed moment of their evolvement; whereas, the evolutionary framework makes it possible to follow the evolution of systems.…”

Section: Introductionmentioning

confidence: 99%

Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

Scrimali

2012

J Optim Theory Appl

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In this paper, we develop an infinite dimensional Lagrangian duality framework for modeling and analyzing the evolutionary pollution control problem. Specifically, we examine the situation in which different countries aim at determining the optimal investment allocation in environmental projects and the tolerable pollutant emissions, so as to maximize their welfare. We state the equilibrium conditions underlying the model, and provide an equivalent formulation in terms of an evolutionary variational inequality. Moreover, by means of infinite dimensional duality tools, we prove the existence of Lagrange multipliers that play a fundamental role in order to describe countries' decision-making processes.

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“…In [12], as well as in this note, the authors consider the possibility that the data in the Walras problem depend on time and introduce a time-dependent variational inequality model of the new problem. The idea of treating equilibrium problems by time-dependent V.I.…”

mentioning

confidence: 99%

Some remarks on the Walras equilibrium problem in Lebesgue spaces

Causa

Raciti

2010

Optim Lett

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Dynamic Walrasian price equilibrium problem: evolutionary variational approach with sensitivity analysis

Cited by 19 publications

References 12 publications

A variational inequality formulation of the environmental pollution control problem

A variational inequality formulation of the environmental pollution control problem

Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

Some remarks on the Walras equilibrium problem in Lebesgue spaces

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