Saddle Point Criteria for Semi-infinite Programming Problems via an $$\eta $$η-Approximation Method

2018 ◽  
pp. 17-28
Author(s):  
Yadvendra Singh ◽  
S. K. Mishra
Keyword(s):  
Saddle Point ◽  
Approximation Method ◽  
Infinite Programming

scholarly journals ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

2006 ◽  
Vol 26 (1) ◽  
pp. 17-24 ◽  
Author(s):  
Zhongping Wan ◽  
Xianjia Wang ◽  
Julin He ◽  
Shihui Jia
Keyword(s):  
Approximation Method ◽  
Asymptotic Approximation ◽  
Infinite Programming

Reliability Analysis of Alumina-Based Ceramic Cutting Tool's Wear Life by Saddle Point Approximation

2013 ◽  
Vol 395-396 ◽  
pp. 979-984
Author(s):  
Xin Gang Wang ◽  
Ya Juan Jin ◽  
Yi Min Zhang
Keyword(s):  
Saddle Point ◽  
Normal Distribution ◽  
Approximation Method ◽  
Cutting Tools ◽  
State Equation ◽  
Ultimate State ◽  
Saddle Point Approximation ◽  
Point Approximation ◽  
Wear Life ◽  
Tools Wear

Under continuous cutting conditions, the reliability of alumina-based ceramic cutting tools wear life with abrasion wear was discussed extensively. An ultimate state equation of alumina-based ceramic cutting tools wear life was proposed according to stress-strength interference theory. Based on the premise that the probability distribution of random parameters has been known, the fracture toughnessKICand the hardnessHwhich obey Weibull distribution were transformed into normal distribution by means of the equivalent normal distribution method, and then the reliability of alumina-based ceramic cutting tools wear life was analyzed by saddle point approximation method. The probability density function and cumulative distribution function of the ultimate state equation were accurately and quickly obtained by way of saddle point approximation, as a result, the saddle point approximation method was proved accurate with high computing speed in comparison with the Monte-Carlo method. Therefore, the application of the saddle point approximation method developed the reliability analysis theory of alumina-based ceramic cutting tools wear life.

scholarly journals Saddle Point Approximation of Mutual Information for Finite-Alphabet Inputs over Doubly Correlated MIMO Rayleigh Fading Channels

2021 ◽  
Vol 11 (10) ◽  
pp. 4700
Author(s):  
Yuyu Liu ◽  
Jinbao Zhang ◽  
Dan Zhang
Keyword(s):  
Mutual Information ◽  
Saddle Point ◽  
Fading Channels ◽  
Approximation Method ◽  
Rayleigh Fading ◽  
Saddle Point Method ◽  
Finite Alphabet ◽  
Rayleigh Fading Channels ◽  
Saddle Point Approximation ◽  
Point Approximation

Given the mutual information of finite-alphabet inputs cannot be calculated concisely and accurately over fading channels, this paper proposes a new method to calculate the mutual information. First, the applicability of the saddle point method is studied, and then the mutual information is estimated by the saddle point approximation method with known channel state information. Furthermore, we induce the expectation of mutual information over doubly correlated multiple-input multiple-output (MIMO) Rayleigh fading channels. The validity of the saddle point approximation method is verified by comparing the numerical results of the Monte Carlo method and the saddle point approximation method under different doubly correlated MIMO fading channel scenarios.

scholarly journals Multitime multiobjective variational problems via η-approximation method

2021 ◽  
pp. 15-15
Author(s):  
Shalini Jha ◽  
Prasun Das ◽  
Sanghamitra Bandhyopadhyay
Keyword(s):  
Saddle Point ◽  
Variational Problem ◽  
Present Article ◽  
Approximation Method ◽  
Optimal Solution ◽  
Variational Problems ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Approximation Approach ◽  
Multiobjective Variational Problems

The present article is devoted to multitime multiobjective variational problems via ?-approximation method. In this method, an ?-approximation approach is applied to the considered problem, and a new problem is constructed, called as ?-approximated multitime multiobjective variational problem that contains the change in objective and both constraints functions. The equivalence between an efficient (Pareto optimal) solution to the main multitime multiobjective variational problem is derived along with its associated ?-approximated problem under invexity defined for a multi- time functional. Furthermore, we have also discussed the saddle-point criteria for the problem considered and its associated ?-approximated problems via generalized invexity assumptions.

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