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First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

Ginchev, Ivan, Ivanov, Vsevolod I. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally...

Fixed points and iterations of mean-type mappings

Janusz Matkowski (2012)

Open Mathematics

Let (X, d) be a metric space and T: X → X a continuous map. If the sequence (T n)n∈ℕ of iterates of T is pointwise convergent in X, then for any x ∈ X, the limit μ T ( x ) = lim n → ∞ T n ( x ) is a fixed point of T. The problem of determining the form of µT leads to the invariance equation µT ○ T = µT, which is difficult to solve in general if the set of fixed points of T is not a singleton. We consider this problem assuming that X = I p, where I is a real interval, p ≥ 2 a fixed positive integer and T is the mean-type mapping...

F-limit points in dynamical systems defined on the interval

Piotr Szuca (2013)

Open Mathematics

Given a free ultrafilter p on ℕ we say that x ∈ [0, 1] is the p-limit point of a sequence (x n)n∈ℕ ⊂ [0, 1] (in symbols, x = p -limn∈ℕ x n) if for every neighbourhood V of x, {n ∈ ℕ: x n ∈ V} ∈ p. For a function f: [0, 1] → [0, 1] the function f p: [0, 1] → [0, 1] is defined by f p(x) = p -limn∈ℕ f n(x) for each x ∈ [0, 1]. This map is rarely continuous. In this note we study properties which are equivalent to the continuity of f p. For a filter F we also define the ω F-limit set of f at x. We consider...

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

Akritas, Alkiviadis, Argyris, Andreas, Strzeboński, Adam (2008)

Serdica Journal of Computing

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate...

F-Normalreihen.

Herbert Möller (1977)

Journal für die reine und angewandte Mathematik

Fonctions de type trace

Daniel Barlet (1983)

Annales de l'institut Fourier

Soit π : V → W un morphisme propre fini et surjectif entre deux variétés analytiques complexes. Nous donnons une caractérisation des fonctions (continues) sur W qui sont de la forme π * f où f est une fonction C ∞ sur V . Pour cela nous introduisons la notion de fonction de type trace sur une variété analytique complexe. Ces fonctions sont analytiques réelles en dehors d’une hypersurface complexe et admettent des singularités très simples aux points de cette hypersurface.

Fonctions séparément analytiques

Jean Saint Raymond (1990)

Annales de l'institut Fourier

On étudie les fonctions de deux variables réelles qui sont séparément analytiques sur un ouvert du plan. On montre que ces fonctions sont analytiques en tout point du domaine de définition hors d’un fermé de ce domaine dont les projections sur chacun des deux axes de coordonnées sont des ensembles polaires. Inversempent, pour tout tel fermé F , on construit une fonction séparément analytique dont le domaine d’analyticité est le complémentaire de F .

Fopid Controller Design for Robust Performance Using Particle Swarm Optimization

Zamani, Majid, Karimi-Ghartemani, Masoud, Sadati, Nasser (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33; 93C15, 93C55, 93B36, 93B35, 93B51; 03B42; 70Q05; 49N05This paper proposes a novel method to design an H∞ -optimal fractional order PID (FOPID) controller with ability to control the transient, steady-state response and stability margins characteristics. The method uses particle swarm optimization algorithm and operates based on minimizing a general cost function. Minimization of the cost function is carried out subject to the H∞ -norm; this norm is also...

Forcing relation on minimal interval patterns

Jozef Bobok (2001)

Fundamenta Mathematicae

Let ℳ be the set of pairs (T,g) such that T ⊂ ℝ is compact, g: T → T is continuous, g is minimal on T and has a piecewise monotone extension to convT. Two pairs (T,g),(S,f) from ℳ are equivalent if the map h: orb(minT,g) → orb(minS,f) defined for each m ∈ ℕ₀ by h ( g m ( m i n T ) ) = f m ( m i n S ) is increasing on orb(minT,g). An equivalence class of this relation-a minimal (oriented) pattern A-is exhibited by a continuous interval map f:I → I if there is a set T ⊂ I such that (T,f|T) = (T,f) ∈ A. We define the forcing relation on...

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