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l-stable Functions and Constrained Optimization ℓ-устойчиви функции и условна оптимизация

Ginchev, Ivan — 2010

Union of Bulgarian Mathematicians

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5]. The class of ℓ-stable at a point functions defined in [2] and being larger than the class of C1,1 functions,...

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

Ginchev, IvanIvanov, 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...

From scalar to vector optimization

Ivan GinchevAngelo GuerraggioMatteo Rocca — 2006

Applications of Mathematics

Initially, second-order necessary optimality conditions and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem φ ( x ) min , x m , are given. These conditions work with arbitrary functions φ m ¯ , but they show inconsistency with the classical derivatives. This is a base to pose the question whether the formulated optimality conditions remain true when the “inconsistent” Hadamard derivatives are replaced with the “consistent” Dini derivatives. It...

Locally Lipschitz vector optimization with inequality and equality constraints

Ivan GinchevAngelo GuerraggioMatteo Rocca — 2010

Applications of Mathematics

The present paper studies the following constrained vector optimization problem: min C f ( x ) , g ( x ) - K , h ( x ) = 0 , where f : n m , g : n p are locally Lipschitz functions, h : n q is C 1 function, and C m and K p are closed convex cones. Two types of solutions are important for the consideration, namely w -minimizers (weakly efficient points) and i -minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x 0 to be a w -minimizer and first-order sufficient conditions for x 0 ...

A note on Minty type vector variational inequalities

Giovanni P. CrespiIvan GinchevMatteo Rocca — 2005

RAIRO - Operations Research - Recherche Opérationnelle

The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced....

A note on Minty type vector variational inequalities

Giovanni P. CrespiIvan GinchevMatteo Rocca — 2006

RAIRO - Operations Research

The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are introduced. Under...

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