• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.595-619
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• 2022

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.135-173
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• 2023

The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.

• Journal of Korean Society of Transportation
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• v.20 no.3
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• pp.129-147
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• 2002

This paper presents a variational equality formulation by Providing new dynamic route choice condition for a link-based dynamic traffic assignment model. The concepts of used paths, used links, used departure times are employed to derive a new link-based dynamic route choice condition. The route choice condition is formulated as a time-dependent variational equality problem and necessity and sufficiency conditions are provided to prove equivalence of the variational equality model. A solution algorithm is proposed based on physical network approach and diagonalization technique. An asymmetric network computational study shows that ideal dynamic-user optimal route condition is satisfied when the length of each time interval is shortened. The I-394 corridor study shows that more than 93% of computational speed improved compared to conventional variational inequality approach, and furthermore as the larger network size, the more computational performance can be expected. This paper concludes that the variational equality could be a promising approach for real-time application of a dynamic traffic assignment model based on fast computational performance.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.2
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• pp.125-137
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• 1995

This paper provides a locally convergent algorithm and a globally convergent algorithm for a variational inequality problem over convex polyhedral. The algorithm are based on the B (ouligand)-differentiability of the solution of a nonsmooth equation derived from the variational in-equality problem. Convergences of the algorithms are achieved by the results of Pang[3].

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.579-592
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• 2000

We study the variational principle for quantum unbounded spin systems interacting via superstable and regular interactions. We show that the (weak) KMS state constructed via the thermodynamic limit of finite volume Green's functions satisfies the Gibbs variational equality.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.1
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• pp.52-63
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• 1983

The purpose of the study is to find development of contact area, contact pressure and friction forces occurring at joints or connection areas inbetween structural members or mechanical parts. The problem has a pair of difficulties intrinsically; a constraint of displacement due to contact, and presence of work term by nonconservative friction force in the variational principle of the problem. Because of these difficulties, the variational principle remains in the form of inequality. It is resolved by penalty method and perturbation method making the inequality to an equality which is proper for computational purposes. A contact problem without friction is solved to find contact area and contact pressure, which are to be used as data for the analysis of the friction problem using perturbed variational principle. For numerical experiments, a Hertz problem, a rigid punch problem, and the latter one with friction effects are solved using $Q_2$-finite elements.

• Nuclear Engineering and Technology
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• v.16 no.4
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• pp.181-194
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• 1984

The in-core fuel management problem was studied by use of the calculus of variations. Two functions of interest to a public power utility, the profit function and the cost function, were subjected to the constraints of criticality, the reactor turnup equations and an inequality constraint on the maximum allowable power density. The variational solution of the initial profit rate demonstrated that there are two distinct regions of the reactor, a constant power region and a minimum inventory or flat thermal flux region. The transition point between these regions is dependent on the relative importance of the profit for generating power and the interest charges for the fuel. The fuel cycle cost function was then used to optimize a three equal volume region reactor with a constant fuel enrichment. The inequality constraint on the maximum allowable power density requires that the inequality become an equality constraint at some points in the reactor. and at all times throughout the core cycle. The finite difference equations for reactor criticality and fuel burnup in conjunction with the equality constraint on power density were solved, and the method of gradients was used to locate an optimum enrichment. The results of this calculation showed that standard non-linear optimization techniques can be used to optimize a reactor when the inequality constraints are properly applied.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.436-439
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• 2005

Dynamic contact of a cantilever beam with Sap at the end is discussed. The gap in a structure induces dynamic contact, and the contact problem is always accompanied by inequality constraints which mean that the solution of the structure with contact condition should satisfy variational inequality. Inequality, but, can be reduced to equality condition considering convex penalty function. In this paper, formulation of a beam with contact is derived using quasi convex penalty function. General coordinate solution which is needed to increase computational efficiency is applied. Nonlinear behavior of a beam with rigid and elastic contact condition was discussed.

• Journal of Korean Society of Transportation
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• v.21 no.6
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• pp.77-88
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• 2003

This paper proposes a solution algorithm for solving a multi-class analytical DTA model. In the DTA model, three traveler classes are classified according to different assumptions of traveler's route choice behavior: including fixed route, Stochastic Dynamic User Optimum(SDUO), and Dynamic User Optimum(DUO). To solve this DTA model, variables of link flow and exit flow are represented solely by inflow. The resulting Linear Program(LP) subproblem in the inner iteration is solved as a typical time-dependent shortest route problem over a physical network. Accordingly, the required time-space network expansion in solving DTA models is no longer needed.

• Journal of Korean Society of Transportation
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• v.20 no.4
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• pp.135-150
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• 2002

The basic assumption of analytical Dynamic Traffic Assignment models is that traffic demand and network conditions are known as a priori and unchanging during the whole planning horizon. This assumption may not be realistic in the practical traffic situation because traffic demand and network conditions nay vary from time to time. The rolling horizon implementation recognizes a fact : The Prediction of origin-destination(OD) matrices and network conditions is usually more accurate in a short period of time, while further into the whole horizon there exists a substantial uncertainty. In the rolling horizon implementation, therefore, rather than assuming time-dependent OD matrices and network conditions are known at the beginning of the horizon, it is assumed that the deterministic information of OD and traffic conditions for a short period are possessed, whereas information beyond this short period will not be available until the time rolls forward. This paper introduces rolling horizon implementation to enable a multi-class analytical DTA model to respond operationally to dynamic variations of both traffic demand and network conditions. In the paper, implementation procedure is discussed in detail, and practical solutions for some raised issues of 1) unfinished trips and 2) rerouting strategy of these trips, are proposed. Computational examples and results are presented and analyzed.