scholarly journals A Method with Convergence Rates for Optimization Problems with Variational Inequality Constraints

2021 ◽  
Vol 31 (3) ◽  
pp. 2171-2198
Author(s):  
Harshal D. Kaushik ◽  
Farzad Yousefian
Keyword(s):  
Variational Inequality ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Inequality Constraints

scholarly journals Well Posedness of New Optimization Problems with Variational Inequality Constraints

2021 ◽  
Vol 5 (3) ◽  
pp. 123
Author(s):  
Savin Treanţă
Keyword(s):  
Variational Inequality ◽  
Lower Semicontinuity ◽  
Optimization Problems ◽  
Integral Functional ◽  
Inequality Constraints ◽  
Multiple Integral ◽  
Well Posedness ◽  
Constrained Optimization Problems ◽  
New Class ◽  
Theoretical Developments

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples.

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

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