جستجوی مقالات مرتبط با کلیدواژه « duality » در نشریات گروه « ریاضی »

In this paper, we state the problem of the network flow interdiction in a set of initial and destination nodes so that each initial is capable of only delivering products to certain pre-determined destinations. The network user’s purpose is to deliver the highest value of flow from the sources to the sinks and the network interdictor’s purpose is to reduce the highest value of flow being used. In this paper, the networks flow interdiction in multi-source and multi-sink conditions are addressed in a way that the parameters of arc capacity are trapezoidal fuzzy sets.

In this study, we explore the theoretical features of a multiobjective interval-valued programming problem with vanishing constraints. In view of this, we have defined a multiobjective interval-valued programming prob-lem with vanishing constraints in which the objective functions are consid-ered to be interval-valued functions, and we define an LU-efficient solution by employing partial ordering relations. Under the assumption of general-ized convexity, we investigate the optimality conditions for a (weakly) LU-efficient solution to a multiobjective interval-valued programming problem with vanishing constraints. Furthermore, we establish Wolfe and Mond–Weir duality results under appropriate convexity hypotheses. The study concludes with examples designed to validate our findings.

In this paper, we introduce a new class of arcwise $\rho$-$K$-connected, arcwise $\rho$-$K$-quasi connected and arcwise $\rho$-$K$-pseudo connected functions which encapsulate already known functions. Necessary and sufficient optimality conditions are established for a vector optimization problem over cones by involving these functions. Wolfe type and Mond-Weir type duals are formulated and corresponding duality results are also proved using these functions.

In data envelopment analysis (DEA) models, the weak disposability axiom has been used for undesirable outputs such as environmental pollutants in many cases. Considering this axiom, different models are exhibited to assess the efficiency of units under evaluation. In this paper, we express duality in weak disposability models proposed by Kousmanen (2005) and Amirteimoori et al. (2017). In the following, economical interpretations of dual are represented in the abovementioned technologies. Also, projection points for inefficient units will be introduced; then, proposed methods will also be explained in an application that includes different designs for the production line of a company.

The aim of this paper is to introduce an abstract notion of determinant which we call quantum determinant, verifying the properties of the classical one. We introduce R−basis and R−solution on rigid objects of a monoidal 𝐴𝑏−category, for a compatibility relation R, such that we require the notion of duality introduced by Joyal and Street, the notion given by Yetter and Freyd and the classical one, then we show that R−solutions over a semisimple ribbon 𝐴𝑏−category form as well a semisimple ribbon 𝐴𝑏−category. This allows us to define a concept of so-called quantum determinant in ribbon category. Moreover, we establish relations between these and the classical determinants. Some properties of the quantum determinants are exhibited.

In this article, we formulate a new mixed-type dual problem for a mathematical program with vanishing constraints. The presented dual problem does not involve the index set, however, the dual models contain the calculations of index sets, which makes it difficult to solve these models from an algorithm point of view. The weak, strong and strict converse duality theorems are discussed in order to establish the relationships between the mathematical program with vanishing constraints and its mixed type dual under generalized convexity. To validate the results, a non-trivial example is discussed. Our dual model unifies the dual models discussed in [Q. Hu, J. Wang, Y. Chen, New dualities for mathematical programs with vanishing constraints, Annals of Operations Research, 287 (2020) 233-255].

In this paper, we first study the non-positive decreasing and inverse co-radiant functions defined on a real locally convex topological vector space X. Next, we characterize non-positive increasing, co-radiant and quasi-concave functions over X. In fact, we examine abstract concavity, upper support set and superdifferential of this class of functions by applying a type of duality. Finally, we present abstract concavity of extended real valued increasing, co-radiant and quasi-concave functions.

As an important duality result in linear optimization, the Goldman–Tucker theorem establishes strict complementarity between a pair of primal and dual linear programs. Our study extends this result into the framework of linear fractional optimization. Associated with a linear fractional program, a dual program can be defined as the dual of the equivalent linear program obtained from applying the Charnes–Cooper transformation to the given program. Based on this definition, we propose new criteria for primal and  dual optimality by showing that the primal and dual optimal sets can be equivalently modeled as the optimal sets of a pair of primal and dual linear programs. Then, we define the concept of strict complementarity and establish the existence of at least one, called strict complementary, pair of primal and dual optimal solutions such that in every pair of comple mentary variables, exactly one variable is positive and the other is zero. We geometrically interpret the strict complementarity in terms of the relative interiors of two sets that represent the primal and dual optimal setsin higher dimensions. Finally, using this interpretation, we develop two approaches for finding a strict complementary solution in linear fractional optimization. We illustrate our results with two numerical examples.

One of the key issues raised in networks flow is its interdiction. Keshavarzi ‎et al. ‎scrutinized the issue with the multi-sources and multi-sinks conditions in mind while considering the specific conditions of flow being sent from sources to sinks ‎[R. Keshavarzi ‎et al.‎, Multi-source-sinks network flow interdiction problem, ‎International Journal of Academic Research,‎ 2015]. Moreover, the matter was also examined in the state of multi-interdictors and a practical solution was presented ‎[‎K‎eshavarzi and, Salehi, Multi commodity multi source-sinks network flow interdiction problem with several interdictors, ‎Journal of Engineering and Applied Sciences,‎ 2015]‎. In this paper, the networks flow interdiction in multi-source and multi-sink conditions was addressed; meanwhile, bearing in mind the uncertain data (from a specified beginning to an ending interval), an optimal interval was presented. Finally, a numerical example for this issue was provided and then solved by the program "Lingo"‎.‎

The motivation behind this paper is to study a class of nondifferentiable multiobjective fractional programming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a differentiable function, we consider the class of second-order (F,alpha,rho,d)-type-I convex functions. Further, we formulate unified (mixed type) dual models and derive duality relations under aforesaid assumptions.

Since it is well-known that the Vandermonde matrix is ill-conditioned, this paper surveys the choices of other bases. These bases are data-dependent and are categorized into discretely $ell^2$-orthonormal  and continuously $L^2$-orthonormal bases. The first one is defined via a decomposition of the Vandermonde matrix while the latter is given by a decomposition of the Gramian matrix corresponding to monomial bases. A discussion of various matrix decomposition (e.g. Cholesky, QR and SVD) provides a variety of different bases with different properties. Special attention is given to duality. Numerical results show that the matrices of values of the new bases have smaller condition numbers than the common monomial bases. It can also be pointed out that the new introduced bases are good candidates for interpolation.

In this paper, we have introduced efficiency of order m for a class of non-differentiable multi-objective variational problems in which every component of the objective and constraint function contains a term involving the square root of a certain positive semidefinite quadratic form. Necessary optimality conditions are obtained for this solution concept . Parametric dual of non-differentiable multi-objective fractional variational problem is proposed. Duality theorems are proved to relate efficient solutions of order m for primal problem and its dual. These results are obtained using generalized

In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.

In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.