scholarly journals A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zezhong Wu ◽  
Jiuping Xu
Keyword(s):  
Genetic Algorithm ◽  
Variational Inequality ◽  
Existence Theorem ◽  
Existence Of A Solution ◽  
Method Of Solution

Invex monotonicity and pseudoinvex monotonicity of fuzzy mappings are introduced in this paper, and relations are discussed between invex monotonicity (pseudoinvex monotonicity) and invexity (pseudoinvexity) of fuzzy mappings. The existence of a solution to the fuzzy variational-like inequality is discussed, and the existence theorem can be achieved. Furthermore, some extended properties of the fuzzy variational-like inequality are researched. Finally, method of solution is discussed based on genetic algorithm.

scholarly journals An Elementary Proof of the Theorems of Cauchy and Mayer

1935 ◽  
Vol 4 (3) ◽  
pp. 112-117
Author(s):  
A. J. Macintyre ◽  
R. Wilson
Keyword(s):  
Differential Equation ◽  
Existence Theorem ◽  
Elementary Proof ◽  
Theoretical Discussion ◽  
Practical Advantage ◽  
Total Differential ◽  
Method Of Solution ◽  
The Subject ◽  
Image Position ◽  
Natural Way

Attention has recently been drawn to the obscurity of the usual presentations of Mayer's method of solution of the total differential equationThis method has the practical advantage that only a single integration is required, but its theoretical discussion is usually based on the validity of some other method of solution. Mayer's method gives a result even when the equation (1) is not integrable, but this cannot of course be a solution. An examination of the conditions under which the result is actually an integral of equation (1) leads to a proof of the existence theorem for (1) which is related to Mayer's method of solution in a natural way, and which moreover appears to be novel and of value in the presentation of the subject.

scholarly journals Some New Classes of Extended General Mixed Quasi-Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Auxiliary Principle ◽  
Existence Of A Solution ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Special Cases ◽  
Quasi Variational Inequality

We consider and study a new class of variational inequality, which is called the extended general mixed quas-variational inequality. We use the auxiliary principle technique to study the existence of a solution of the extended general mixed quasi-variational inequality. Several special cases are also discussed. Results proved in this paper may stimulate further research in this area.

scholarly journals A general vector-valued variational inequality and its fuzzy extension

1998 ◽  
Vol 21 (4) ◽  
pp. 637-642 ◽  
Author(s):  
Sehie Park ◽  
Byung-Soo Lee ◽  
Gue Myung Lee
Keyword(s):  
Variational Inequality ◽  
Existence Theorem ◽  
Kkm Theorem ◽  
Vector Valued ◽  
General Vector

A general vector-valued variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form of KKM theorem due to Park. Moreover, we obtain the fuzzy extension of our existence theorem.

scholarly journals Monte Carlo Sampling Method for a Class of Box-Constrained Stochastic Variational Inequality Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Pei-Yu Li
Keyword(s):  
Monte Carlo ◽  
Variational Inequality ◽  
Optimization Problem ◽  
Sampling Method ◽  
Monte Carlo Sampling ◽  
Merit Function ◽  
Variational Inequality Problems ◽  
Sufficient Condition ◽  
Existence Of A Solution ◽  
Stochastic Variational Inequality

This paper uses a merit function derived from the Fishcher–Burmeister function and formulates box-constrained stochastic variational inequality problems as an optimization problem that minimizes this merit function. A sufficient condition for the existence of a solution to the optimization problem is suggested. Finally, this paper proposes a Monte Carlo sampling method for solving the problem. Under some moderate conditions, comprehensive convergence analysis is included as well.

scholarly journals On a complementarity problem associated with nondifferentiable programming

1984 ◽  
Vol 25 (3) ◽  
pp. 419-430 ◽  
Author(s):  
B. D. Craven ◽  
B. Mond ◽  
J. Parida
Keyword(s):  
Existence Theorem ◽  
Stationary Point ◽  
Complementarity Problem ◽  
Optimal Solution ◽  
Nondifferentiable Programming ◽  
Regularity Conditions ◽  
Point Problem ◽  
Nonlinear Program ◽  
Existence Of A Solution

AbstractThis paper deals with the question of the existence of a solution to the stationary-point problem corresponding to a given nonlinear nondifferentiable program. An existence theorem for the stationary-point problem is presented under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the nonlinear program.

scholarly journals On the placing of synchronized vector measurements in network 110 - 330 kV for identification of the Kaliningrad region power system regime

2018 ◽  
Vol 58 ◽  
pp. 01005
Author(s):  
Magomed Gadzhiev ◽  
Eugenia Gulevich ◽  
Vyacheslav Korobka ◽  
Vladimir Ryabchenko ◽  
Yuriy Sharov
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Power System ◽  
Electric Power ◽  
Electric Power System ◽  
Phasor Measurement Unit ◽  
Measurement Unit ◽  
Method Of Solution ◽  
Kaliningrad Region ◽  
The Mathematical Model

A solution is presented for the problem of placing phasor measurement unit to identify the mathematical model of the electric power system in the state space. The criterion for complete observability of the Kalman dynamic system is taken as a basis. As a method of solution, we use the canonical genetic algorithm. The complete observability of the power system is ensured by the application of the observability rule in the form of a recursive test of observability. The proposed approach is demonstrated by the arrangement of synchronized vector meters in the Kaliningrad region power system.

scholarly journals Existence of a solution of the quasi-variational inequality with semicontinuous operator

2006 ◽  
Vol 16 (2) ◽  
pp. 147-152
Author(s):  
Djurica Jovanov
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Existence Of A Solution ◽  
Feasible Set ◽  
Quasi Variational Inequality

The paper considers quasi-variational inequalities with point to set operator. The existence of a solution, in the case when the operator of the quasi-variational inequality is semi-continuous and the feasible set is convex and compact, is proved.

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