A variational inequality formulation of the environmental pollution control problem

Scrimali, Laura

doi:10.1007/s11590-009-0165-2

Cited by 20 publications

(7 citation statements)

References 29 publications

(37 reference statements)

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“…We first note that, as proved in [29], a vector (e * i (t), I * i (t)) ∈ K i is an optimal solution to problem (7) if and only if it is a solution of the following variational inequality, for each i = 1, . .…”

Section: Theorem 33 Let Us Assume That Assumptions Of Theorem 32 Bementioning

confidence: 98%

“…In this section, we present the evolutionary environmental pollution control problem and give the equilibrium conditions governing the model (see also [6,7,29]). We study the system in the finite time horizon [0, t], with t > 0.…”

Section: The Modelmentioning

confidence: 99%

“…. , N: (14) It is beyond the scope of this paper to discuss existence or regularity results for problem (14); however, we refer to [21,29,42,43] for further analysis.…”

Section: Theorem 33 Let Us Assume That Assumptions Of Theorem 32 Bementioning

confidence: 99%

“…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%

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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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Section: Theorem 33 Let Us Assume That Assumptions Of Theorem 32 Bementioning

confidence: 98%

Section: The Modelmentioning

confidence: 99%

“…. , N: (14) It is beyond the scope of this paper to discuss existence or regularity results for problem (14); however, we refer to [21,29,42,43] for further analysis.…”

Section: Theorem 33 Let Us Assume That Assumptions Of Theorem 32 Bementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

Scrimali

2012

J Optim Theory Appl

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“…Recently, Qiang et al (2013) used the theory to consider a closed-loop supply chain network. Scrimali (2010) used it to discuss the environmental pollution control problem. Other applications can be found in the works of Ban et al (2012), Wakolbinger and Cruz (2011) and Cruz and Matsypura (2009).…”

Section: Solution Approachmentioning

confidence: 99%

Supply chain equilibrium among companies with offline and online selling channels

Han

Jie

et al. 2015

International Journal of Production Research

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This study proposes a supply chain system model containing Nash game companies that compete in a common market. Each company adopts a vertical integration strategy and runs offline and online selling channels. To maximise profits, the companies determine optimal production quantities and prices. Using theory of finite-dimensional variational inequality, we prove the existence and uniqueness of the equilibrium pattern and develop a converged algorithm. Numerically, we compute the equilibrium production quantities and prices, and subsequently generate three findings through sensitivity analyses. By changing the transportation cost, we demonstrate that the offline price is conditionally higher than the online price with different transportation and processing costs. All equilibrium prices and profits decrease when substitution intensity is increased, and thus companies should differentiate their products. Altering consumer preference for online purchasing shows that consumer preference significantly influences the production quantities and profits. Online selling is not positively affected by consumer preference for online purchasing but is affected by the complex relationship between consumer preference and its variable cost.

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Variational Methods for Emerging Real–Life and Environmental Conservation Problems

Scrimali

Maugeri

2019

Differential and Integral Inequalities

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A variational inequality formulation of the environmental pollution control problem

Cited by 20 publications

References 29 publications

Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

Supply chain equilibrium among companies with offline and online selling channels

Variational Methods for Emerging Real–Life and Environmental Conservation Problems

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