Displaying similar documents to “A generalization of the quasiconvex optimization problem.”

On dual vector optimization and shadow prices

Letizia Pellegrini (2010)

RAIRO - Operations Research


In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying Lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices.

Penalties, Lagrange multipliers and Nitsche mortaring

Christian Grossmann (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization


Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.

On constraint qualifications in directionally differentiable multiobjective optimization problems

Giorgio Giorgi, Bienvenido Jiménez, Vincente Novo (2010)

RAIRO - Operations Research


We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the functions are differentiable. The relationships between them are analyzed. Finally, we give...

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,...