ε-Regularized two-level optimization problems: Approximation and existence results

2006 ◽  
pp. 99-113 ◽  
Author(s):  
P. Loridan ◽  
J. Morgan
Keyword(s):  
Optimization Problems ◽  
Existence Results

Symmetry of solutions to optimization problems related to partial differential equations

2006 ◽  
Vol 136 (5) ◽  
pp. 921-934 ◽  
Author(s):  
Fabrizio Cuccu ◽  
Giovanni Porru
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Optimization Problems ◽  
Existence Results ◽  
Dirichlet Problems ◽  
Partial Differential ◽  
Moving Plane Method ◽  
Plane Method ◽  
Moving Plane

We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving-plane method to find symmetry results for solutions of a system. We apply these results in our discussion of symmetry for the maximal configurations of the previous problem.

scholarly journals GENERALIZED IMPLICIT INCLUSION PROBLEMS ON NONCOMPACT SETS WITH APPLICATIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 261-279
Author(s):  
SAN-HUA WANG ◽  
NAN-JING HUANG
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Existence Results ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Inclusion Problems ◽  
Topological Vector Spaces ◽  
Vector Equilibrium

AbstractIn this paper, a class of generalized implicit inclusion problems is introduced, which can be regarded as a generalization of variational inequality problems, equilibrium problems, optimization problems and inclusion problems. Some existence results of solutions for such problems are obtained on noncompact subsets of Hausdorff topological vector spaces using the famous FKKM theorem. As applications, some existence results for vector equilibrium problems and vector variational inequalities on noncompact sets of Hausdorff topological vector spaces are given.

scholarly journals Existence of optimal shapes under a uniform ball condition for geometric functionals involving boundary value problems

2020 ◽  
Vol 26 ◽  
pp. 108
Author(s):  
Jérémy Dalphin
Keyword(s):  
Shape Optimization ◽  
Mean Curvature ◽  
Obstacle Problem ◽  
Optimization Problems ◽  
Existence Results ◽  
Quadratic Growth ◽  
Normal Vector ◽  
Boundary Values ◽  
Optimal Shapes ◽  
Fluid Membranes

In this article, we are interested in shape optimization problems where the functional is defined on the boundary of the domain, involving the geometry of the associated hypersurface (normal vector n, scalar mean curvature H) and the boundary values of the solution uΩ related to the Laplacian posed on the inner domain Ω enclosed by the shape. For this purpose, given ε > 0 and a large hold-all B ⊂ ℝn, n ≥ 2, we consider the class Oε(B) of admissible shapes Ω ⊂ B satisfying an ε-ball condition. The main contribution of this paper is to prove the existence of a minimizer in this class for problems of the form infΩ∈Oε(B) ∫ ∂Ωj[uΩ(x),∇uΩ(x),x,n(x),H(x)]dA(x). We assume the continuity of j in the set of variables, convexity in the last variable, and quadratic growth for the first two variables. Then, we give various applications such as existence results for the configuration of fluid membranes or vesicles, the optimization of wing profiles, and the inverse obstacle problem.

Comparison of Meta-heuristic Algorithms on Benchmark Functions

2019 ◽  
Vol 2 (3) ◽  
pp. 508-517
Author(s):  
FerdaNur Arıcı ◽  
Ersin Kaya
Keyword(s):  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Time Interval ◽  
Bee Colony ◽  
Different Characteristics

Optimization is a process to search the most suitable solution for a problem within an acceptable time interval. The algorithms that solve the optimization problems are called as optimization algorithms. In the literature, there are many optimization algorithms with different characteristics. The optimization algorithms can exhibit different behaviors depending on the size, characteristics and complexity of the optimization problem. In this study, six well-known population based optimization algorithms (artificial algae algorithm - AAA, artificial bee colony algorithm - ABC, differential evolution algorithm - DE, genetic algorithm - GA, gravitational search algorithm - GSA and particle swarm optimization - PSO) were used. These six algorithms were performed on the CEC’17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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