1,721,024 research outputs found
Massimo della somma tra una funzione lineare ed una funzione lineare fratta
No full textWe present a sequential method to solve a constrained extrema problem with feasible region defined by linear inequalities and objective function expressed as a sum of a linear and homografical functions. The technique used finds a finite number of local extrema, the last being the global one. © 1985 Springer-Verlag
Lagrange multipliers and generalized differentiable functions in vector extremum problems
No full textIn this paper, we establish a necessary optimality condition for a nondifferentiable vector extremum problem which involves a generalized vector-valued Lagrangian function. Such a condition is stated for a wide class of functions, which embraces the differentiable ones and a subclass of locally Lipschitzian functions. The condition embodies the classic theorem of F. John in multiobjective optimization
REGULARITY CONDITIONS FOR CONSTRAINED EXTREMUM PROBLEMS
No full textNecessary and/or sufficient conditions are stated in order to have regularity for nondifferentiable problems or differentiable problems. These conditions are compared with some known constraint qualifications
Some results on regularity in vector optimization
No full textIn this paper we suggest an approach to regularity in vector optimization; some necessary or sufficient regularity conditions are given for a wide class of nondifferentiable vector optimization problems which embraces the convex ones
Stationary points and necessary conditions in vector extremum problems
No full textThe concept of lower limit for a real-valued function is extended to vector optimization; the vector lower limit allows us to propose a definition of a vector lower semi-stationary point which extends the concept of critical Pareto point. The study of the strict connection between a lower semi-stationary point and a local vector minimum point permits us to obtain necessary and/or sufficient optimality conditions for non differentiable multiobjective functions, which assume a simple form in the differentiable case.
Some of these results are characterized to Pareto vector problems and to the scalar case in order to obtain known conditions and new ones
The Sum of a Linear and a Linear Fractional Function: Pseudoconvexity on the Nonnegative Orthant and Solution Methods
Full text linkThe aim of the paper is to present sequential methods for a pseudoconvex optimization problem whose objective function is the sum of a linear and a linear fractional function and the feasible region is a polyhedron, not necessarily compact. Since the sum of a linear and a linear fractional function is not in general pseudoconvex, we first derive conditions characterizing its pseudoconvexity on the nonnegative orthant. We prove that the sum of a linear and a linear fractional function is pseudoconvex if and only if it assumes particular canonical forms. Then, theoretical properties regarding the existence of a minimum point and its location are established, together with necessary and sufficient conditions for the infimum to be finite. The obtained results allow us to suggest simplex- like sequential methods for solving optimization problems having as objective function the proposed canonical forms
On the maximal domains of pseudoconvexity of a quadratic fractional function
No full textIn this paper we will characterize the maximal domains of pseudoconvexity of the ratio betwcen a quadratic function and an affine one. Furthermore, motivated by thc fact that in optimization problems the decision variables are often required to be nonnegative, we will specialize the obtained results in order to achieve conditions which guarantee that the nonnegative orthant is contained in thc maximal domains
of pseudoconvexity of the function
Equivalence in linear fractional programming
No full textIn this paper two algorithms are suggested for solving a linear fractional problem whatever the feasible region is. Such algorithms can be interpreted as a modified version of Martos and Charnes-Cooper algorithms. Successively, it will be shown that the two methods are algorithmically equivalent in the sense that they generate the same finite sequence of points leading to an optimal solution. This last result can be viewed as an extension of the one given by Wagner-Yuan for a compact feasible region
On the pseudoconvexity and pseudolinearity of some classes of fractional functions
Full text linkThe aim of the article is to study the pseudoconvexity (pseudoconcavity) of the ratio between a quadratic function and the square of an affine function. Applying the Charnes–Cooper transformation of variables the function is transformed in a quadratic one defined on a suitable halfspace. The characterization of the pseudoconvexity of such a quadratic function allows to give necessary and sufficient conditions for the pseudoconvexity and the pseudolinearity of the ratio in terms of the initial data
- …
