Quasi-tangent vectors in flow-invariance and optimization problems on Banach manifolds

In the setting of Banach manifolds the notion of tangent vector to an arbitrary closed subset has been introduced in [11] by the author and N. H. Pavel, and it has been used in flow-invariance and optimization ([11], [12], [13]). For detailed informations on tangent vectors to closed sets (including historical comments) we refer to the recent book of N. H. Pavel [17].The aim of this paper is to apply this general concept of tangency in the study of geodesies. We are concerned with geodesies which have either the endpoints in given closed subsets or the same angle for a fixed closed subset. This approach allows one to extend important results due to K. Grove [4] and T. Kurogi ([6], [7]).

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Tangent Cones and Convexity

Canadian Mathematical Bulletin ◽

10.4153/cmb-1976-040-x ◽

1976 ◽

Vol 19 (3) ◽

pp. 257-261 ◽

Cited By ~ 13

Author(s):

J. Borwein ◽

R. O’Brien

Keyword(s):

Constrained Optimization ◽

Optimization Problems ◽

Tangent Cones ◽

Constrained Optimization Problems ◽

Multiplier Theorems ◽

Tangent Vectors

The study of general multiplier theorems (Kuhn-Tucker Conditions) for constrained optimization problems has led to extensions of the notion of a differentiable arc. Abadie [1], Varaiya [10], Guignard [5], Zlobec [11] and Massam [12] investigated the so called cone of tangent vectors to a point in a set for optimization purposes.

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Comparison of Meta-heuristic Algorithms on Benchmark Functions

Academic Perspective Procedia ◽

10.33793/acperpro.02.03.41 ◽

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&rsquo;17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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