scholarly journals A REMARK ON THE REGULARIZED GAP FUNCTION FOR IQVI

2015 ◽  
Vol 28 (1) ◽  
pp. 145-150
Author(s):  
Sangho Kum
Keyword(s):  
Gap Function ◽  
Regularized Gap Function

scholarly journals Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hui-Qiang Ma ◽  
Nan-Jing Huang
Keyword(s):  
Sample Average Approximation ◽  
Gap Function ◽  
Stationary Points ◽  
Quasivariational Inequality ◽  
Minimization Method ◽  
Limiting Behavior ◽  
Regularized Gap Function ◽  
Expected Residual Minimization ◽  
Sample Average ◽  
Residual Minimization

We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points.

scholarly journals On Gap Functions for Quasi-Variational Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Kouichi Taji
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Gap Function ◽  
Gap Functions ◽  
Merit Functions ◽  
Regularized Gap Function ◽  
Generalized Equilibrium ◽  
Quasi Variational Inequality

For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable.

AVERAGE SIZE OF GAPS IN THE FOURIER EXPANSION OF MODULAR FORMS

2007 ◽  
Vol 03 (02) ◽  
pp. 207-215 ◽  
Author(s):  
EMRE ALKAN
Keyword(s):  
Elliptic Curve ◽  
Modular Forms ◽  
Fourier Expansion ◽  
Complex Multiplication ◽  
Gap Function ◽  
Quantitative Results ◽  
Average Size

We prove that certain powers of the gap function for the newform associated to an elliptic curve without complex multiplication are "finite" on average. In particular we obtain quantitative results on the number of large values of the gap function.

DDC Lubrication: A New Concept in Tribology

1992 ◽  
Vol 114 (1) ◽  
pp. 181-185 ◽  
Author(s):  
K. To̸nder
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Gap Function ◽  
Upper And Lower Bounds ◽  
Roughness Effects ◽  
Cavity Depth ◽  
Roughness Amplitude ◽  
Previously Treated ◽  
The Mean ◽  
Expansion Scheme

A new lubrication concept is presented, Deep Disconnected Cavities. It differs from the lubrication of microcavities, previously treated by other authors, by the deepness of the cavities. The validity of Reynolds’ equation and nonturbulent conditions are assumed. By a Taylor expansion scheme, it is shown that the roughness effects are expressible in terms of roughness factors modifying the Reynolds equation, similar to those proposed by Patir and Cheng (1978). Unlike those established for ordinary roughness, the DDC factors are independent of local film thickness and roughness amplitude (cavity depth), and may therefore be used to modify standard hydro-dynamic parameters. By a different mathematical approach, involving upper and lower bounds on the various hydrodynamic quantities, it is found that Reynolds’ equation and all the other hydrodynamic expressions may be written just as for smooth surfaces, with the following modifications: 1. The film thickness should be expressed by the minimum gap function, and not by the mean gap function. 2. There are, in general, three effective viscosities, lower than the physical one, two of which are associated with the x and y directions respectively and appear in the modified Reynolds equation as well as in the flow terms. The third one appears only in the expression for shear stress.

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