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In this paper, a new pair of higher-order nondifferentiable multiobjective mixed symmetric dual programs over arbitrary cones is formulated, where each of the objective functions contains a support function of a compact convex set. Usual duality theorems are established under higher-order K- (F , α , ρ , d) -convexity assumptions. Also, the example of a higher-order dual pair, which shows that higher-order provides tighter bounds for the value of the objective function of the primal and dual problem, is given in the paper. Several known results are also discussed as special cases. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified Tseng's extragradient method with a new step-length rule to solve pseudo-monotone variational inequalities in real Hilbert spaces. Under suitable conditions, the sequence generated by this algorithm strongly converges to the common elements of the solution set of pseudo-monotone variational inequality problems and the fixed point set of k-demicontractive mappings. Finally, we give some numerical experiments to illustrate the effectiveness of the proposed algorithm. The main results of this paper generalize and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

The growing use of optimization models to help decision making has created a demand for such tools that allow formulating and solving more models of real-world processes and systems related to human activity in which hypotheses are not verify in a way specific for classical optimization. One of the approaches for real-world extremum problems under uncertainty is interval-valued optimization. In this paper, a twice differentiable vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. In this paper, the first order necessary optimality conditions of Karush-Kuhn-Tucker type are proved for differentiable interval-valued vector optimization problems under the first order constraint qualification. If the interval-valued objective function is assumed to be twice weakly differentiable and constraints functions are assumed to be twice differentiable, then two types of second order necessary optimality conditions under two various constraint qualifications are proved for such smooth interval-valued vector optimization problems. Finally, in order to illustrate the Karush-Kuhn-Tucker type necessary optimality conditions established in the paper, an example of an interval-valued optimization is given. [ABSTRACT FROM AUTHOR]

In this paper, we develop different types of strategic alliance and business cooperation between different decision-making units (DMUs) based on ratio-based data envelopment analysis (DEA-R) models. In this regard, two DMUs as partners share some of their input components in order to improve their performance in the partnership process. This is possible when a DMU has a surplus of resources in an input component, while another DMU has a shortage of resources in this component, and this adjustment of resources is done in a way to improve the performance of both DMUs. In the following, we present the inverse DEA-R models in order to determine the optimal level of some input and output components from two DMUs in the process of partnerships as partners, in order to reach the target efficiency level for each of these DMUs. Considering that DEA-R models have a larger space than weights based on the ratio of input to output components (and vice versa), therefore we expect the presented DEA-R models to have a higher discriminating power in the selection of weights compared to data envelopment analysis (DEA) models, then DEA-R models avoid pseudo-inefficiency and efficiency underestimation issues and achieve potential gains for DMUs in the process of partnerships in a competitive market. We present an application of the proposed approach to the data set of 70 banks operating in the European Union and show that these banks can improve their performance based on the optimal strategy presented. [ABSTRACT FROM AUTHOR]

Abdessamad Oussarhana and Tijani AmahroqbaLIMATI Laboratory, Poly-disciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco; bLAMAI Laboratory, Faculty of Sciences and Techniques, Cadi Ayyad University, Marrakech, Morocco We provide a counterexample to Proposition 2.3 in our paper [Optimization 20, 69(12), pp. 2611–2627] where we said that the convex set A and the element $ x_0 $ x 0 can be properly separated by a closed hyperplane if $ x_0\notin {\rm pri}(A) $ x 0 ∉ pri (A) , with $ {\rm pri}(A) $ pri (A) is the pseudo relative interior of A. In addition, we re-establish all results rely on this proposition, more precisely, [Amahroq and Oussarhan Infinite-dimensional vector optimization and a separation theorem. Optimization. 2020;69(12):2611–2627, Lemma 2.1 (ii)–(iv)], [Amahroq and Oussarhan Infinite-dimensional vector optimization and a separation theorem. Optimization. 2020;69(12):2611–2627, Theorem 3.1] and [Amahroq and Oussarhan Infinite-dimensional vector optimization and a separation theorem. Optimization. 2020;69(12):2611–2627, Corollary 5.1] (see Section 1). A revision to the proof of [Amahroq and Oussarhan Infinite-dimensional vector optimization and a separation theorem. Optimization. 2020;69(12):2611–2627, Theorem 4.1] is also done (see Section 2). We claim that, the rest of the paper (Amahroq and Oussarhan Infinite-dimensional vector optimization and a separation theorem. Optimization. 2020;69(12):2611–2627) is independent of the above incorrect statements. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of approximate Benson properly efficient solutions for the set-valued equilibrium problems (in short, SVEP) and investigate its properties. Under some suitable assumptions, the linear scalarization theorems for SVEP are obtained. Two nonlinear scalarization theorems for SVEP are presented. Based on the linear scalarization results, the nonemptiness and connectedness of the approximate Benson properly efficient solution set are established under some suitable conditions in real locally convex spaces. Some examples are also given to illustrate our results. The main results of this paper improve and generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the solution of generalized vector bifunction variational inequalities of Stampachhia and Minty types with the concept of generalized cone. Existence results have been established over compact and non-compact sets in Banach spaces without using convexity condition on a bifunction. Some relationship between generalized vector bifunction variational inequalities and vector optimization problems have been established. [ABSTRACT FROM AUTHOR]

Berge's notion of equilibrium represents a complementary alternative to the Nash equilibrium when modeling socioeconomic behavior and human interactions. While the notion of Nash equilibrium is based on self-interest, as players seek to maximize their own payoffs given the action of the other players, the idea behind Berge equilibrium is mutual support, as given the action of one of the players, all others select their actions looking for her best interest. However, because of the demanding conditions involved, the existence of Berge equilibria is rarely guaranteed. In this paper, we propose vector-valued normal-form games as a unified framework in which to study and extend the concept of Berge equilibrium. Based on the equilibria of the so-called altruistic game, we introduce new equilibrium concepts which constitute different relaxations of Berge's notion, although they still retain the underlying idea of mutual support. We establish the links between these new equilibria, Nash equilibrium, Berge equilibrium, and other related concepts already existing in the literature. Our approach has the advantage that it permits the incorporation of preference information to identify the equilibria which are consistent with different altruistic attitudes of the players. [ABSTRACT FROM AUTHOR]

This paper peruses one of the most challenging healthcare concerns related to human organ transplantation. In this regard, a medical system's health-economic objectives are investigated to (1) achieve a desirable level of health equity in offering healthcare services to patients who are differentiated in terms of medical conditions, and (2) minimize total costs incurred across managing the inventory. This paper presents the first-ever operational research study to manage processed corneal tissue (PCT). Besides, hybrid demand-oriented policies have been proposed to equitably issue and assign specific inventories to demands with distinct medical urgent levels (ULs). In this regard, a practical multi-objective mixed-integer linear programming (MOMILP) model is proposed for a system with multiple products that can be substituted with each other according to medical priorities. A goal programming (GP) approach is utilized to find the optimum solution. The applicability of the model is validated through a real case study. Finally, several sensitivity analyses are conducted to examine the effect of critical parameters on the solutions to gain useful managerial insights. The results show that the proposed health-economic trade-off is well performed and can efficiently handle the real case. [ABSTRACT FROM AUTHOR]

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 illustrate this with some examples. In addition, we obtain solutions to the interval equilibrium problem in the unconstrained case. The results presented in this paper extend the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

This paper gives verifiable conditions for the existence of solutions of some set quasi-optimization problems involving Minkowski difference, where the objective maps are defined in complete metric spaces. Our proof method is not based on any scalarizing approach, and our existence results are written in terms of the given data of the problems. Several examples are provided. As applications of the main results of this paper, new results on the existence of robust solutions for uncertain multi-objective quasi-optimization problems with set-valued maps are formulated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new classes of higher order generalized strong invex functions under non-differentiable settings. The optimality results are derived for higher order strict global minimizers of non-differentiable multiobjective programming problems using these functions. Numerical examples and illustrations are provided in support of new classes of functions and the optimality conditions. We also study the mixed dual problem and establish weak, strong and converse duality results. Furthermore, as an application, we present a non-differentiable case of vector variational-like inequality problem and establish the equivalence between its solutions and higher order strict global minimizers of the non-differentiable multiobjective programming problem. [ABSTRACT FROM AUTHOR]

The multi-objective integer programming problem often occurs in multi-criteria decision-making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the globally proper efficiency of set optimization problems. Firstly, we use the so-called certainly set less order relation to define a new kind of set order relation. Based on the new set order relation, we introduce the notion of the globally proper efficient solution of the set optimization problem. Secondly, we establish Lagrange multiplier rule of the set optimization problem. Finally, we obtain Lagrangian duality theorems and saddle point theorems. We also give some examples to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper we consider multi-objective optimization problems over a box. Several computational approaches to solve these problems have been proposed in the literature, that broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and retrieving good solutions even in the nonconvex case, and descent methods, which excel in efficiently approximating good quality solutions. In this paper, first we confirm, through numerical experiments, the advantages and disadvantages of these approaches. Then we propose a new method which combines the good features of both. The resulting algorithm, which we call Non-dominated Sorting Memetic Algorithm, besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions. [ABSTRACT FROM AUTHOR]

This paper provides a study of multiobjective fractional variational programs involving support functions. It then explains the concept of higher-order K– η convex. The paper's motivation is to study the duality results for the value of primal and dual programs. The numerical example of functional is discussed, which is higher-order K– η convex but not first-order K– η convex. A real-world example is considered to verify the results of the weak duality theorem. [ABSTRACT FROM AUTHOR]

Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimization problems even for specific cases. In this paper, we study set-valued optimization problems and develop a multiobjective optimization problem that is strongly related to it. We prove that the set of weakly minimal solutions of this subproblem is closely related to the set of weakly minimal elements of the set-valued optimization problem and that these sets can get arbitrarily close in a certain sense. Subsequently, we introduce a concept of approximations of the solution set of the set-valued optimization problem. We define a quality measure in the image space that can be used to compare finite approximations of this kind and outline a procedure to enhance a given approximation. We conclude the paper with some numerical examples. [ABSTRACT FROM AUTHOR]

This paper is devoted to second-order optimality conditions of constrained vector optimization problems with continuously Fréchet differentiable data. Different from conventional approaches, we employ a new one, image space analysis, to establish suitable regularity conditions and then present new second-order necessary optimality conditions that depend on one single KKT multiplier for all critical directions. Moreover, we propose one more regularity condition for the multiobjective case and compare it with the previous one. Besides, we compare the main regularity conditions with the existing ones in the literature for the scalar case. [ABSTRACT FROM AUTHOR]

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalarization has been widely studied, but providing accelerated methods with accurate proofs of convergence rates remains an open problem. Our proposed method is a multiobjective generalization of the accelerated proximal gradient method, also known as the Fast Iterative Shrinkage-Thresholding Algorithm, for scalar optimization. The key to this successful extension is solving a subproblem with terms exclusive to the multiobjective case. This approach allows us to demonstrate the global convergence rate of the proposed method ( O (1 / k 2) ), using a merit function to measure the complexity. Furthermore, we present an efficient way to solve the subproblem via its dual representation, and we confirm the validity of the proposed method through some numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we are mainly concerned with a rule for efficient (Pareto) approximate subdifferential, concerning the sum of two cone-convex set-valued vector mappings, taking values in finite or infinite-dimensional preordred spaces. The obtained formula is exact and holds under the connectedness or Attouch-Brézis qualification conditions and the regular subdifferentiability. This formula is applied to establish approximate necessary and sufficient optimality conditions for the existence of the approximate Pareto (weak or proper) efficient solutions of a set-valued vector optimization problem. [ABSTRACT FROM AUTHOR]

This paper presents exact dual semi-definite programs (SDPs) for robust SOS-convex polynomial optimization problems with affinely adjustable variables in the sense that the optimal values of the robust problem and its associated dual SDP are equal with the solution attainment of the dual problem. This class of robust convex optimization problems includes the corresponding quadratically constrained convex quadratic optimization problems and separable convex polynomial optimization problems, and it employs a general bounded spectrahedron uncertainty set that covers the most commonly used uncertainty sets of numerically solvable robust optimization models, such as boxes, balls and ellipsoids. As special cases, it also demonstrates that explicit exact dual SDP and second-order cone programming (SOCP) in terms of original data hold for the robust two-stage convex quadratic programs with quadratic constraints and the robust two-stage separable convex quadratic programs under an ellipsoidal uncertainty set, respectively. Finally, the paper illustrates the results via numerical implementations of the developed SDP duality scheme on adjustable robust lot-sizing problems with nonlinear costs under demand uncertainty. [ABSTRACT FROM AUTHOR]

As resources are valuable assets, organizations have to decide which resources to allocate to business process tasks in a way that the process is executed not only effectively but also efficiently. Traditional role-based resource allocation leads to effective process executions, since each task is performed by a resource that has the required skills and competencies to do so. However, the resulting allocations are typically not as efficient as they could be, since optimization techniques have yet to find their way in traditional business process management scenarios. On the other hand, operations research provides a rich set of analytical methods for supporting problem-specific decisions on resource allocation. This paper provides a novel framework for creating transparency on existing tasks and resources, supporting individualized allocations for each activity in a process, and the possibility to integrate problem-specific analytical methods of the operations research domain. To validate the framework, the paper reports on the design and prototypical implementation of a software architecture, which extends a traditional process engine with a dedicated resource management component. This component allows us to define specific resource allocation problems at design time, and it also facilitates optimized resource allocation at run time. The framework is evaluated using a real-world parcel delivery process. The evaluation shows that the quality of the allocation results increase significantly with a technique from operations research in contrast to the traditional applied rule-based approach. [ABSTRACT FROM AUTHOR]

A new methodology is proposed in this paper to solve multiobjective optimisation problems (MOPs) by invoking genetic algorithms and solutions concepts of cooperative games. The weighting problems that are formulated by assigning some suitable weights to the multiple objective functions are usually solved to obtain the Pareto optimal solutions of MOPs. In this paper, the suitable weights will be taken from the core values of a cooperative game that is formulated from the original MOP by regarding the objective functions as players. Under these settings, we shall obtain a large set of all so-called Core-Pareto optimal solutions. In order to choose the best Core-Pareto optimal solution from this set, we shall invoke the genetic algorithms by setting a reasonable fitness function. [ABSTRACT FROM AUTHOR]

In this paper, we study and develop robust nonsmooth optimality conditions and duality analysis for an uncertain multiobjective programming problem with constraints ((UCMOP), for brevity). First, we introduce the constraint qualification of the (GRSCQ) type and then establish some robust necessary optimality conditions in terms of the generalized subdifferentials for some types of minima (including robust weakly efficient and robust properly efficient) to such problem involving stable functions. Under suitable assumptions on the pseudo-convexity of objective and constraint functions, robust necessary nonsmooth optimality conditions become robust sufficient optimality conditions. An application of the obtained results for its Wolfe and Mond–Weir types dual problem is presented and some illustrative examples are also provided for our findings. [ABSTRACT FROM AUTHOR]