Rufián-Lizana Antonio

• PhD
• Professor (Full) at University of Seville

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending the results from the literature. We i...

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending results from the literature. We intro...

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 conce...

This paper aims to obtain new Karush–Kuhn–Tucker optimality conditions for solutions to semi-infinite interval equilibrium problems with interval-valued objective functions. The Karush–Kuhn–Tucker conditions for the semi-infinite interval programming problem are particular cases of those found in this paper for constrained equilibrium problem. We i...

Solving a perishable food distribution problem in a real world setting is a very complex task. This is due to products characteristics, and the requirements of customers. To ensure a safe, quality product with a desired service level, a bunch of specifications should be included during the decision/optimization process. Generally, it’s difficult to...

This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated...

This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustr...

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points be global minimums. In order to do so, we extend th...

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend...

This article provides a new characterization of the switching points for generalized Hukuhara differentiability and shows that the set of all switching points is at most countable. Using these results, new properties in differential calculus, which generalize previous results, are presented. Then, generalizations of Ostrowski type inequalities for...

In this article we present new results on the sum of gH-differentiable fuzzy functions . We give conditions so that the sum of two gH-differentiable fuzzy functions become gH-differentiable. We present also practical rules for obtaining the gH-derivative of the sum of fuzzy functions.

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different co...

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different co...

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 and Interval Variational-like Inequality Problems, both Stampacchia and Minty type. Pseudo invex monotonicity condit...

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 literat...

In De Campos Ibáñez and González-Muñoz (Fuzzy Sets Syst 29:145–154, 1989, [6]), Goestschel and Voxman (Fuzzy Sets Syst 18:31–43, 1986, [7]) the authors considered a linear ordering on the space of fuzzy intervals. For each fuzzy mapping (fuzzy interval-valued mapping) F, based on the aforementioned linear ordering, they introduced a real-valued fun...

In this article we present a new concept of stationary point for gH-differentiable fuzzy functions which generalize previous concepts that exist in the literature. Also, we give a concept of generalized convexity for gH-differentiable fuzzy functions more useful than level-wise generalized convexity (generalized convexity of the endpoint functions)...

This paper aims to study magnesium composites with reinforcement of cerium oxide. For this, Mg-CeO2 composites were produced by powder metallurgy, with variations of 1%, 2% and 4% by weight of reinforcement. The temperature used was 620°C for a time of 6h. These materials were metallographically analyzed by means of optical microscopy, SEM and EDS,...

In this article we study efficiency and weakly efficiency in fuzzy vector optimization. After formulating the problem, we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized Hukuhara differentiability, pseudoinvexity-I and pseudoinvexity-II. We prove that pseudoinvexity is the necessary and suffici...

In this paper we define a new minimum concept for fuzzy optimization problems more general than those that exist in the literature. We find necessary optimality conditions based on a new fuzzy stationary point definition. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions.

The aim of this paper is to show some applicable results to multiobjective optimization problems and the role that the Generalized Convexity plays in them. The study of convexity for sets and functions has special relevance in the search of optimal functions, and in the development of algorithms for solving optimization problems. However, the absen...

The aim of this paper is to show one of the generalized convexity applications, generalized monotonicity particularly, to the variational problems study. These problems are related to the search of equilibrium conditions in physical and economic environments. If convexity plays an important role in mathematical programming problems, monotonicity wi...

This paper considers optimization problems with fuzzy-valued objective functions. For this class of fuzzy optimization problems we obtain Karush-Kuhn-Tucker type optimality conditions considering the concept of generalized Hukuhara differentiable and pseudo-invex fuzzy-valued functions.

In this article we consider optimization problems where the objectives are fuzzy functions (fuzzy-valued functions). For this class of fuzzy optimization problems we discuss the Newton method to find a non-dominated solution. For this purpose, we use the generalized Hukuhara differentiability notion, which is the most general concept of existing di...

Jeyakumar (Methods Oper. Res. 55:109–125, 1985) and Weir and Mond (J. Math. Anal. Appl. 136:29–38, 1988) introduced the concept of preinvex function. The preinvex functions have some interesting properties. For example, every local minimum of a preinvex function is a global minimum and nonnegative linear combinations of preinvex functions are prein...

In this paper, we study the relationships between the Stampacchia and Minty vector variational inequalities and vector continuous-time programming problems under generalized invexity and monotonicity hypotheses. We extend the results given by other authors for the scalar case to vectorial one, and we show the equivalence of efficient and weak effic...

The properties of minimum φ-divergence estimators for parametric multinomial populations are well-known when the assumed parametric model is true, namely, they are consistent and asymptotically normally distributed. Here we study these properties when the parametric model is not assumed to be correctly specified. Under certain conditions, these est...

In this paper, we study generalized convexity for fuzzy mappings that are defined through a linear ordering on the space of fuzzy intervals. On top of the concepts of convexity, preinvexity and prequasiinvexity, which have been introduced previously by other authors, we now introduce the concept of invex fuzzy mappings. For this purpose, we first c...

This paper addresses the optimization problems with interval-valued objective function. For this we consider two types of order relation on the interval space. For each order relation, we obtain KKT conditions using of the concept of generalized Hukuhara derivative ( $gH$ -derivative) for interval-valued functions. The $gH$ -derivative is a conc...

This paper is devoted to studying differential calculus for interval-valued functions by using the generalized Hukuhara differentiability, which is the most general concept of differentiability for interval-valued functions. Conditions, examples and counterexamples for limit, continuity, integrability and differentiability are given. Special emphas...

We study the minimal solutions in a nondifferentiable multiobjective problem, using a relation induced by a cone C, that is C-efficient and C-weakly efficient solutions. First of all, a new class of nondifferentiable vector functions, named (C1,C2)-pseudoinvex, is introduced pointing out that it differs from the ones already proposed in the literat...

In this paper, we first show the need for introducing invex fuzzy mappings. After that, we show that the concept of invex fuzzy mapping previously given by Wu and Xu are very restrictive and the examples presented there are not correct. Then, we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differen...

In this paper, we provide new pseudoinvexity conditions on the involved functionals of a multiobjective variational problem, such that all vector Kuhn-Tucker or Fritz John points are weakly efficient solutions if and only if these conditions are fulfilled. We relate weakly efficient solutions to optimal solutions of weighting problems. We improve r...

Necessary conditions of optimality are presented for weakly efficient solutions to multiobjective minimization problems with inequality-type constraints. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions and they are based on the concept of 2-regularity introduced by Izmailov. In general, the op...

This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach spaces under pseudo-invexity and pseudo-monotonicity hypotheses. We have extended the results given by Gang and Liu...

In this paper, we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem, called W-KT-pseudoinvexity and W-FJ-pseudoinvexity. We prove that all Kuhn–Tucker or Fritz–John points are weakly efficient solutions if and only if these conditions are fulfilled. We relate weakly efficient solutions to optimal so...

We prove that in order for the Kuhn–Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions that we introduce here: KT-pseudoinvex-II or FJ-pseudoinvex-II, respectively. We illustrate it by examples. These characterizations...

In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to establish duality results, but it is also necessary. Moreover, these functions are characterized in order that all Kuhn-Tucker or Frit...

Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The...

We present new classes of vector invex and pseudoinvex functions which generalize the class of scalar invex functions. These new classes of vector functions are characterized in such a way that every vector critical point is an efficient or a weakly efficient solution of a Multiobjective Programming Problem. We establish relationships between these...

Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The...

This paper introduces a new condition on the functionals of a control problem and extends a recent characterization result of KT-invexity. We prove that the new condition, the FJ-invexity, is both necessary and sufficient in order to characterize the optimal solution set using Fritz John points.

In this paper, we introduce a new condition on functionals involved in a multiobjective control problem, for which we define the V-KT-pseudoinvex control problem. We prove that a V-KT-pseudoinvex control problem is characterized so that a Kuhn–Tucker point is an efficient solution. We generalize recently obtained optimality results of known mathema...

In this paper, we introduce new classes of vector functions which generalize the class of scalar invex functions. We prove that these new classes of vector functions are characterized in such a way that every vector critical point is an efficient solution of a Multiobjective Programming Problem. We establish relationships between these new classes...

In this paper we study the existence of weakly efficient solutions for some nonsmooth and nonconvex vector optimization problems. We consider problems whose objective functions are defined between infinite and finite-dimensional Banach spaces. Our results are stated under hypotheses of generalized convexity and make use of variational-like inequali...

In this work, we will establish some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces under invexity hy- potheses. This paper extends the earlier work of Ruiz-Garzon et al. (7).

In this paper, we introduce a new condition on functions of a control problem, for which we define a KT-invex control problem. We prove that a KT-invex control problem is characterized in order that a Kuhn–Tucker point is an optimal solution. We generalize optimality results of known mathematical programming problems. We illustrate these results wi...

In this paper, we establish characterizations for efficient solutions to multiobjective programming problems, which generalize the characterization of established results for optimal solutions to scalar programming problems. So, we prove that in order for Kuhn–Tucker points to be efficient solutions it is necessary and sufficient that the multiobje...

We study the equivalence between the solutions of the variational-like inequality problem and the solutions of certain nonsmooth and nonconvex vectorial optimization problem.

In this work, we introduce the notion of preinvex function for functions between Banach spaces. By using these functions, we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities. Moreover, we will show that this class of problems has the property that each local optimal solution is in fac...

In this paper we will establish the relationships between vector variational-like inequality and optimization problems. We will be able to identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality problem, under conditions of pseudo invexity. These conditions are more general t...

Sometimes, to locate efficient solutions for multiobjective variational problems (MVPs) is quite costly, so in this paper we tackle the study of weakly efficient solutions for MVPs. A new concept of weak vector critical point which generalizes other ones already existent, and a new class of pseudoinvex functions are introduced. We will apply a new...

In this paper the generalized invex monotone functions are defined as an extension of monotone functions. A series of sufficient and necessary conditions are also given that relate the generalized invexity of the function θ with the generalized invex monotonicity of its gradient function ∇θ. This new class of functions will be important in order to...

In this paper we study the saddle point optimality conditions and Lagrange duality in multiobjective optimization for generalized subconvex-like functions. We obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solut...

During the last years numerous results about optimality in mathematical programming problems with generalized convex functions have been obtained, with special attention to multiobjetive problems. In this paper, we consider multiobjective problems with ρ- convex functions and some additional hypothesis. The objective is to deduce theoretical prope...

This paper derives several results regarding the optimality conditions and duality properties for the class of multiobjective fractional programs under generalized convexity assumptions. These results are obtained by applying a parametric approach to reduce the problem to a more conventional form.

For the scalar programming problem, some characterizations for optimal solutions are known. In these characterizations convexity properties play a very important role. In this work, we study characterizations for multiobjective programming problem solutions when functions belonging to the problem are differentiable. These characterizations need som...

Martin (Ref. 1) studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Kuhn–Tucker points (depending on the case) remains true if we optimize several...

D. H. Martin studied the optimality conditions of invex functions in the scalar case. In this work we will generalize his results making them applicable to the vectorial case. We will prove that equivalences between minima and stationary points are still true if we have to optimize p-objective functions instead of one objective function.

In this work we consider the unconstrained multiobjective quadratic problem with strictly convex objective functions, (PCM — D). Firstly we expose a technique to determine the equations of the efficient points supposing that there are only two objective functions. This method is based on results on quadratic forms withdrawals by Gantmacher. Secondl...

In this paper, we study a characterization of weakly efficient solutions of Multiobjective Optimization Problems (MOPS). We find that, under some quasiconvex conditions of the objective functions in a convex set of constraints, weakly efficient solutions of an MOP can be characterized as an optimal solution to a scalar constraint problem, in which...

Using the definition of ray in Euclidean space, we define a new class of functions that avoid Karamardian’s anomaly and which contain the quasi- monotonic functions. These new functions have a good behaviour in relation to its optimal sets, allowing the construction of heuristic algorithms in order to find its extreme points.

In this work we use the notion of vectorial critical point and Karush-Kuhn-Tucker critical point for some class of vectorial optimization problems between Banach spaces. By using these notions, we obtain a characterization for weakly efficient solutions for such optimization problems.

In this work, we study the equivalence between the solutions of variational-like inequality problem and the solutions of some nonsmooth, non-convex vectorial op-timization problem.

In this work, we establish optimality conditions for the nonsmooth multiobjective fractional programming. Also, we give some duality results.

In this work we introduce the notion of pre-invex function for functions between Banach spaces. By using these functions, we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities. Moreover, we will show that this class of problems has the property that all local optimal solution is in fact...

En este trabajo se propone la utilización de distribuciones estadísticas discretas como alternativa a la distribución lognormal para la modelización de datos de disimilaridad provenientes de escalas con pocas modalidades en los modelos confirmatorios MDS de Ramsay y Vera. Los resultados ponen de manifiesto que las distribuciones más apropiadas son...