scholarly journals Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

2012 ◽  
pp. 179-191 ◽  
Author(s):  
L. B. Santos ◽  
M. A. Rojas-Medar ◽  
V. A. Oliveira
Keyword(s):  
Multiobjective Optimization ◽  
Saddle Point ◽  
Second Order

Reliability Analysis by Mean-Value Second-Order Expansion

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Deshun Liu ◽  
Yehui Peng
Keyword(s):  
Saddle Point ◽  
Limit State ◽  
Quadratic Function ◽  
Mean Value ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
Chi Square ◽  
Normal Distributions ◽  
Independent Variables

In this paper, two second-order methods are proposed for reliability analysis. First, general random variables are transformed to standard normal random variables. Then, the limit-state function is additively decomposed into one-dimensional functions, which are then expanded at the mean-value point to second-order terms. The approximated limit-state function becomes the sum of independent variables following noncentral chi-square distributions or normal distributions. The first method computes the probability of failure by the saddle-point approximation. If a saddle-point does not exist, the second method is then used. The second method approximates the limit-state function by a quadratic function with independent variables following normal distributions with the same variances. This treatment leads to a quadratic function that follows a noncentral chi-square distribution. These methods generally produce more accurate reliability approximations than the first-order reliability method (FORM) with 2n + 1 function evaluations, where n is the dimension of the problem. The effectiveness of the proposed methods is demonstrated with three examples, and the proposed methods are compared with the first- and second-order reliability methods (SROMs).

On the Fritz John saddle point problem for differentiable multiobjective optimization

OPSEARCH ◽  
2016 ◽  
Vol 53 (4) ◽  
pp. 917-933
Author(s):  
Maria C. Maciel ◽  
Sandra A. Santos ◽  
Graciela N. Sottosanto
Keyword(s):  
Multiobjective Optimization ◽  
Saddle Point ◽  
Saddle Point Problem ◽  
Point Problem

Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Xiaoxia Yang ◽  
Haibo Chen
Keyword(s):  
Dynamical System ◽  
Saddle Point ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Saddle Point Theorem ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Existence Of Periodic Solutions

AbstractIn this paper, some existence theorems are obtained for periodic solutions of second order dynamical system with (q, p)-Laplaician by using the least action principle and the saddle point theorem. Our results improve Pasca and Tang’ results.

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