222 research outputs found
Second-order optimality conditions for interval-valued functions
This work is included in the search of optimality conditions for solutions to the scalar
interval optimization problem, both constrained and unconstrained, by means of
second-order optimality conditions. As it is known, these conditions allow us to reject
some candidates to minima that arise from the first-order conditions. We will define
new concepts such as second-order gH-derivative for interval-valued functions,
2-critical points, and 2-KKT-critical points. We obtain and present new types of
interval-valued functions, such as 2-pseudoinvex, characterized by the property that
all their second-order stationary points are global minima. We extend the optimality
criteria to the semi-infinite programming problem and obtain duality theorems.
These results represent an improvement in the treatment of optimization problems
with interval-valued functions.Funding for open access publishing: Universidad de Cádiz/CBUA. The research has been supported by MCIN through
grant MCIN/AEI/PID2021-123051NB-I00
New optimality conditions for multiobjective fuzzy programming problems
In this paper we study fuzzy multiobjective optimization problems de ned for n variables. Based on a new p-dimensional fuzzy stationary-point de nition, necessary e ciency conditions are obtained. And we prove that these conditions are also su cient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general di erentiability hypothesis.The research in this paper has been supported by Fondecyt-Chile, project 1151154 and by Ministerio de Economía y
Competitividad, Spain, through grant MINECO/FEDER(UE) MTM2015-66185-P
Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions
This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5] from our viewpoint of robust Lipschitzian stability. We present meaningful interpretations and practical examples of such models. The main results establish necessary optimality conditions for a broad class of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. The results obtained are new in both smooth and nonsmooth settings of semi-infinite and infinite programming
Solving ill-posed bilevel programs
This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem
The continuous-time problem with interval-valued functions: applications to economic equilibrium
The aim of this paper is to define the Continuous-Time Problem
in an interval context and to obtain optimality conditions for this
problem. In addition, we will find relationships between solutions
of Interval Continuous-Time Problem (ICTP) and Interval Variationallike
Inequality Problems, both Stampacchia and Minty type. Pseudo
invex monotonicity condition ensures the existence of solutions
of the (ICTP) problem. These results generalize similar conclusions
obtained in Euclidean or Banach spaces inside classical mathematical
programming problems or Continuous-Time Problems. We will finish
generalizing the existence of Walrasarian equilibrium price model
and the Wardrop’s principle for traffic equilibrium problem to an
environment of interval-valued functions.The research in this paper has been partially supported by Ministerio de Economía y Competitividad,
Spain, through grant MTM2015-66185-P and Proyectos I+D 2015 MTM2015-66185-P
(MINECO/FEDER) and Fondecyt, Chile, grant 1151154
A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets
In this paper, we deal with the resolution of a fuzzy multiobjective programming problem
using the level sets optimization. We compare it to other optimization strategies studied until now
and we propose an algorithm to identify possible Pareto efficient optimal solutions
Optimality and duality on Riemannian manifolds
Our goal in this paper is to translate results on function classes that are
characterized by the property that all the Karush-Kuhn-Tucker points are efficient solutions, obtained in Euclidean spaces to Riemannian manifolds. We give two new characterizations, one for the scalar case and another for the vectorial case, unknown in this subject literature. We also obtain duality results and give examples to illustrate it.Ministerio de Economía y Competitivida
Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Complete Order Relation
This article explores fundamental properties of convex interval-valued
functions defined on Riemannian manifolds. The study employs generalized
Hukuhara directional differentiability to derive KKT-type optimality conditions
for an interval-valued optimization problem on Riemannian manifolds. Based on
type of functions involved in optimization problems, we consider the following
cases:
1. objective function as well as constraints are real-valued;
2. objective function is interval-valued and constraints are real-valued;
3. objective function as well as contraints are interval-valued.
The whole theory is justified with the help of examples. The order relation
that we use throughout the paper is a complete order relation defined on the
collection of all closed and bounded intervals in
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