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Atid Kangtunyakarn - One of the best experts on this subject based on the ideXlab platform.
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strong convergence theorem for the modified generalized Equilibrium Problem and fixed point Problem of strictly pseudo contractive mappings
Fixed Point Theory and Applications, 2014Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:The purpose of this paper is to modify the generalized Equilibrium Problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong convergence theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized Equilibrium Problem. Moreover, using our main result, we obtain the additional results related to the generalized Equilibrium Problem.
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the combination of the set of solutions of Equilibrium Problem for convergence theorem of the set of fixed points of strictly pseudo contractive mappings and variational inequalities Problem
Fixed Point Theory and Applications, 2013Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:For the purpose of this article, we introduce a new Problem using the concept of Equilibrium Problem and prove the strong convergence theorem for finding a common element of the set of fixed points of an infinite family of κi-strictly pseudo contractive mappings and of a finite family of the set of solutions of Equilibrium Problem and variational inequalities Problem. Furthermore, we utilize our main theorem for the numerical example.
Sarawut Suwannaut - One of the best experts on this subject based on the ideXlab platform.
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strong convergence theorem for the modified generalized Equilibrium Problem and fixed point Problem of strictly pseudo contractive mappings
Fixed Point Theory and Applications, 2014Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:The purpose of this paper is to modify the generalized Equilibrium Problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong convergence theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized Equilibrium Problem. Moreover, using our main result, we obtain the additional results related to the generalized Equilibrium Problem.
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the combination of the set of solutions of Equilibrium Problem for convergence theorem of the set of fixed points of strictly pseudo contractive mappings and variational inequalities Problem
Fixed Point Theory and Applications, 2013Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:For the purpose of this article, we introduce a new Problem using the concept of Equilibrium Problem and prove the strong convergence theorem for finding a common element of the set of fixed points of an infinite family of κi-strictly pseudo contractive mappings and of a finite family of the set of solutions of Equilibrium Problem and variational inequalities Problem. Furthermore, we utilize our main theorem for the numerical example.
Shlomo Bekhor - One of the best experts on this subject based on the ideXlab platform.
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investigating path based solution algorithms to the stochastic user Equilibrium Problem
Transportation Research Part B-methodological, 2005Co-Authors: Shlomo Bekhor, Tomer ToledoAbstract:Abstract This paper focuses on path-based solution algorithms to the stochastic user Equilibrium (SUE) and investigates their convergence properties. Two general optimization methods are adapted to solve the logit SUE Problem. First, a method that closely follows the Gradient Projection (GP) algorithm developed for the deterministic Problem is derived. While this method is very efficient for the deterministic user Equilibrium Problem, we use a simple example to illustrate why it is not suitable for the SUE Problem. Next, a different variant of gradient projection, which exploits special characteristics of the SUE solution, is presented. In this method the projection is on the linear manifold of active constraints. The algorithms are applied to solve simple networks. The examples are used to compare the convergence properties of the algorithms with a path-based variant of the Method of Successive Averages (MSA) and with the Disaggregate Simplicial Decomposition (DSD) algorithm.
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route choice models used in the stochastic user Equilibrium Problem a review
Transport Reviews, 2004Co-Authors: Joseph N Prashker, Shlomo BekhorAbstract:Several route choice models are reviewed in the context of the stochastic user Equilibrium Problem. The traffic assignment Problem has been extensively studied in the literature. Several models were developed focusing mainly on the solution of the link flow pattern for congested urban areas. The behavioural assumption governing route choice, which is the essential part of any traffic assignment model, received relatively much less attention. The core of any traffic assignment method is the route choice model. In the wellknown deterministic case, a simple choice model is assumed in which drivers choose their best route. The assumption of perfect knowledge of travel costs has been long considered inadequate to explain travel behaviour. Consequently, probabilistic route choice models were developed in which drivers were assumed to minimize their perceived costs given a set of routes. The objective of the paper is to review the different route choice models used to solve the traffic assignment Problem. Focus ...
Carmela Vitanza - One of the best experts on this subject based on the ideXlab platform.
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On the study of the economic Equilibrium Problem through preference relations
Journal of Mathematical Analysis and Applications, 2019Co-Authors: Monica Milasi, Alessandra Puglisi, Carmela VitanzaAbstract:Abstract In this paper we consider a competitive economic Equilibrium Problem where preferences of consumers are expressed by means of a binary relation. The aim is to find a suitable quasi-variational inequality which characterizes the equilibria and, by using tools of variational theory, to study such equilibria. The novelty of this paper consists in the study of an economic Equilibrium Problem by a variational approach without the need of representing the consumer's preferences by a utility function.
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Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem
Journal of Inequalities and Applications, 2009Co-Authors: Maria Bernadette Donato, Monica Milasi, Carmela VitanzaAbstract:The aim of this paper is to consider a dynamic competitive economic Equilibrium Problem in terms of maximization of utility functions and of excess demand functions. This Equilibrium Problem is studied by means of a time-dependent quasivariational inequality which is set in the Lebesgue space Open image in new window . This approach allows us to obtain an existence result of time-dependent Equilibrium solutions.
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quasi variational approach of a competitive economic Equilibrium Problem with utility function existence of Equilibrium
Mathematical Models and Methods in Applied Sciences, 2008Co-Authors: Maria Bernadette Donato, Monica Milasi, Carmela VitanzaAbstract:A Walrasian pure exchange economy with utility functions, a particular case of a general economic Equilibrium Problem, is considered in this paper. We assume that each agent is endowed with goods and maximizes his utility function, under his budget constraints. We are able to characterize the Walrasian equilibria as solution of an associated quasi-variational inequality. This approach allows us to obtain an existence result of Equilibrium solutions. As an application, we provide the explicit Equilibrium in the case of two agents and two goods.
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Sensitivity analysis for time dependent spatial price Equilibrium Problem
Mathematics and Computers in Simulation, 2006Co-Authors: Maria Bernadette Donato, Monica Milasi, Carmela VitanzaAbstract:We present some sensitivity results for the spatial price Equilibrium Problem in the case of quantity formulation model and in presence of excess supply and excess demand. The Equilibrium conditions that describe the above model are expressed in terms of a time dependent variational inequality. The variational inequality formulation plays a fundamental role in order to achieve the sensitivity results.
Anthony Chen - One of the best experts on this subject based on the ideXlab platform.
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a self adaptive gradient projection algorithm for the nonadditive traffic Equilibrium Problem
Computers & Operations Research, 2012Co-Authors: Anthony Chen, Zhong ZhouAbstract:Gradient projection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic Equilibrium Problem with additive route costs. Recently, GP has been extended to solve the nonadditive traffic Equilibrium Problem (NaTEP), in which the cost incurred on each route is not just a simple sum of the link costs on that route. However, choosing an appropriate stepsize, which is not known a priori, is a critical issue in GP for solving the NaTEP. Inappropriate selection of the stepsize can significantly increase the computational burden, or even deteriorate the convergence. In this paper, a self-adaptive gradient projection (SAGP) algorithm is proposed. The self-adaptive scheme has the ability to automatically adjust the stepsize according to the information derived from previous iterations. Furthermore, the SAGP algorithm still retains the efficient flow update strategy that only requires a simple projection onto the nonnegative orthant. Numerical results are also provided to illustrate the efficiency and robustness of the proposed algorithm.
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Modeling Physical and Environmental Side Constraints in Traffic Equilibrium Problem
International Journal of Sustainable Transportation, 2011Co-Authors: Anthony Chen, Zhong Zhou, Seungkyu RyuAbstract:ABSTRACT The traffic Equilibrium Problem plays an important role in urban transportation planning and management. It predicts vehicular flows on the transportation network by assigning travel demands given in terms of an origin-destination trip table to routes in a network according to some behavioral route choice rules. In this paper, we enhance the realism of the traffic Equilibrium Problem by explicit modeling various physical and environment restrictions as side constraints. These side constraints are a useful means for describing queuing and congestion effects, restraining traffic flows to limit the amount of emissions, and modeling different traffic control policies. A generalized side-constrained traffic Equilibrium (GSCTE) model is presented and some characterizations of the Equilibrium solutions are discussed. The model is formulated as a variational inequality Problem and solved by a predictor-corrector decomposition algorithm. Two numerical experiments are conducted to demonstrate some properti...
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solving the bicriteria traffic Equilibrium Problem with variable demand and nonlinear path costs
Applied Mathematics and Computation, 2010Co-Authors: Anthony Chen, Dongjoo Park, Will ReckerAbstract:In this paper, we present an algorithm for solving the bicriteria traffic Equilibrium Problem with variable demand and nonlinear path costs. The path cost function considered is comprised of two attributes, travel time and toll, that are combined into a nonlinear generalized cost. Travel demand is determined endogenously according to a travel disutility function. Travelers choose routes with the minimum overall generalized costs. The algorithm involves two components: a bicriteria shortest path routine to implicitly generate the set of non-dominated paths and a projection and contraction method to solve the nonlinear complementarity Problem (NCP) describing the traffic Equilibrium Problem. Numerical experiments are conducted to demonstrate the feasibility of the algorithm to this class of traffic Equilibrium Problems.
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traffic Equilibrium Problem with route specific costs formulation and algorithms
Transportation Research Part B-methodological, 2000Co-Authors: Anthony ChenAbstract:Abstract Using a new gap function recently proposed by Facchinei and Soares [Facchinei, F., Soares, J., 1995. Testing a new class of algorithms for nonlinear complementarity Problems. In: Giannessi, F., Maugeri, A. (Eds.), Variational Inequalities and Network Equilibrium Problems. Plenum Press, New York], we convert the nonlinear complementarity Problem (NCP) formulation for the traffic Equilibrium Problem to an equivalent unconstrained optimization. This equivalent formulation uses both route flows and the minimum origin–destination travel costs as the decision variables. Two unique features of this formulation are that: (i) it can model the traffic assignment Problem with a general route cost structure; (ii) it is smooth, unconstrained, and that every stationary point of the minimization corresponds to a global minimum. These properties permit a number of efficient algorithms for its solution. Two solution approaches are developed to solve the proposed formulation. Numerical results using a route-specific cost structure are provided and compared with the classic traffic Equilibrium Problem, which assumes an additive route cost function.
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reformulating the traffic Equilibrium Problem via a smooth gap function
Mathematical and Computer Modelling, 2000Co-Authors: Anthony ChenAbstract:This paper proposes an alternate formulation of the traffic assignment Problem using route flows and the shortest Origin-Destination (OD) travel times as the decision variables. This is accomplished through defining a gap function to convert the Nonlinear Complementarity Problem (NCP) formulation to an equivalent Mathematical Program (MP). This formulation has two advantages: 1.(i) it can model assignment Problems with general route costs which cannot be accomplished with existing formulations that use link-flow variables 2.(ii) the objective function is smooth, convex, and bounded, which permits efficient MP algorithms for its solution. Two solution approaches are developed to solve the proposed formulation. The first is based on a set of working routes, which are modeled as ''known a priori'' based on travelers' preferences or interviews. The second approach uses a column generation procedure to generate a new route in each iteration on a need basis. For each approach, we use a Successive Quadratic Programming (SQP) algorithm to solve for the solutions. To show that the formulation is correct, we solve a small example with a general route cost and compare it to the classic traffic Equilibrium Problem which assumes an additive route cost function. Finally, numerical results for a medium-sized network are provided to demonstrate the feasibility of the solution approach.
