Wyniki wyszukiwania - BazTech

1

Second-order optimality conditions in nonsmooth vector optimization

Yadav Priyanka

Control and Cybernetics

|

2023

|

Vol. 52, No. 1

35--51

EN

In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.

2

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity

Kailey Navdeep, Sethi Sonali, Saini Shivani

Control and Cybernetics

|

2022

|

Vol. 51, No. 1

71--88

EN

There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (p, r)-ρ-(η, θ)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-ρ-(η, θ)- invex functions but not in the class of (1,−1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.

3

Set-valued minimax fractional programming problems under -cone arcwise connectedness

Das Koushik

Control and Cybernetics

|

2022

|

Vol. 51, No. 1

43--69

EN

In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ- cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.

4

The domination over time and its discretisation

Abbasnezhad Nazanin, Mehri-Takmeh Javad, Vakili Javad

Operations Research and Decisions

|

2020

|

Vol. 30, No. 1

5--24

EN

Domination in graphs is well known and has been an extensively researched branch of graph theory. Since the variation over time is one of the important properties of real-world networks, we study the influence of time on the domination problem. In this paper, we introduce the domination over time problem, including time delay on arcs. Then, an optimal solution to its discretisation is obtained, which is the solution of the original problem.

5

The Duality of Classical Intersection and Union Types

Downen Paul, Ariola Zena M., Ghilezan Silvia

Fundamenta Informaticae

|

2019

|

Vol. 170, nr 1-3

39--92

EN

For a long time, intersection types have been admired for their surprising ability to complete the simply typed lambda calculus. Intersection types are an example of an implicit typing feature which can describe program behavior without manifesting itself within the syntax of a program. Dual to intersections, union types are another implicit typing feature which extends the completeness property of intersection types in the lambda calculus to full-fledged programming languages. However, the formalization of union types can easily break other desirable meta-theoretical properties of the type system. But why should unions be troublesome when their dual, intersections, are not? We look at the issues surrounding the design of type systems for both intersection and union types through the lens of duality by formalizing them within the symmetric language of the classical sequent calculus. In order to formulate type systems which have all of our properties of interest—soundness, completeness, and type safety—we also look at the impact of evaluation strategy on typing. As a result, we present two dual type systems—one for call-by-value and one for call-by-name evaluation—which have all three properties. We also consider the possibility of classical non-deterministic evaluation, for which there is a choice between two different systems depending on which properties are desired: a full type system which is complete, and a simplified type system which is sound and type safe.

6

Determination of Approaches for Project Costs Minimization with Use of Dual Problems

Chernov S., Titov S., Chernova L., Kunanets N., Chernova L.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

|

2019

|

Vol. 8, No 2

61--68

EN

For determining ways of company development, ensuring the growth of profit in manufacture and sales of certain products, it has been proposed to use an algorithm of constructing a problem being inverse to primal-dual one, for minimization of the project costs. The primal and the inverse problems contribute to improving the efficiency of calculation when determining approaches for minimization of costs. This pair of problems is mutually conjugate. The proposed rigorous approach to obtaining the algorithm of constructing a dual problem is based on the following statement: a problem being inverse to a dual one is a primal (original) problem. The authors have proposed and rigorously proven the algorithm of a general approach to the construction of conjugate problem pairs. Formalization of the algorithm developed allows obtaining easily correct pairs of known dual problems. This permitted proposing and proving the truth of the algorithm of constructing a dual problem for the arbitrary form of a primal problem representation.

7

On the multiobjective control problem

Kumar P., Sharma B.

Journal of Applied Analysis

|

2018

|

Vol. 24, nr 2

223--231

EN

In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a numer of examples. It is shown with the help of an example that this class is more general than the existing class of functionals.Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.

8

Optimality conditions and duality for generalized fractional minimax programming involving locally Lipschitz (b,Ψ,Φ,ρ) -univex functions

Antczak T., Mishra S. K., Upadhyay B. B.

Control and Cybernetics

|

2018

|

Vol. 47, no. 1

5--32

EN

In this paper, we are concerned with optimality conditions and duality results of generalized fractional minimax programming problems. Suﬃcient optimality conditions are established for a class of nondiﬀerentiable generalized fractional minimax programming problems, in which the involved functions are locally Lipschitz (b,Ψ,Φ,ρ)-univex. Subsequently, these optimality conditions are utilized as a basis for constructing various parametric and nonparametric duality models for this type of fractional programming problems and proving appropriate duality theorems.

9

Aggregation and related functions in fuzzy set theory: dualities and monotonicity-based generalizations

Mesiar R., Kolesarova A.

Journal of Automation Mobile Robotics and Intelligent Systems

|

2017

|

Vol. 11, No. 3

58--61

EN

We discuss several extensions of binary Boolean functions acting on the domain [0, 1]. Formally, there are 16 disjoint classes of such functions, covering a majority of binary functions considered in fuzzy set theory. We introduce and discuss dualities in this framework, stressing the links between different subclasses of considered functions, e.g., the link between conjunctive and implication functions. Special classes of considered functions are characterized, among others, by particular kinds of monotonicity. Relaxing these constraints by considering monotonicity in one direction only, we generalize standard classes of aggregation functions, implications, semicopulas, etc., into larger classes called pre-aggregations, pre-implications, pre-semicopulas, etc. Note that the dualities discussed for the standard classes also relate the new extended classes of pre-functions.

10

Duality for Quasilattices and Galois Connections

Romanowska A. B., Smith J. D. H.

Fundamenta Informaticae

|

2017

|

Vol. 156, nr 3/4

331--359

EN

The primary goal of the paper is to establish a duality for quasilattices. The main ingredients are duality for semilattices and their representations, the structural analysis of quasilattices as Płonka sums of lattices, and the duality for lattices developed by Hartonas and Dunn. Lattice duality treats the identity function on a lattice as a Galois connection between its meet and join semilattice reducts, and then invokes a duality between Galois connections and polarities. A second goal of the paper is a further examination of this latter duality, using the concept of a pairing to provide an algebraic equivalent to the relational structure of a polarity.

11

Specific duality and stability of positive electrical circuits

Kaczorek T.

Archives of Electrical Engineering

|

2017

|

Vol. 66, nr 4

663--679

EN

The specific duality and asymptotic stability of the positive linear electrical circuits are addressed. The specific duality of positive linear electrical circuits composed of resistances, inductances, capacitances and source voltages is established. 1) The linear electrical circuits are positive if and only if the common branches between meshes with resistances and inductances and meshes with resistances and capacitances contain only source voltages; 2) In linear electrical circuits the interchanges of the inductances by the capacitances and the capacitances by inductances do not change the asymptotic stability of the electrical circuits. The asymptotic stability of the positive and nonpositive electrical circuits is analyzed.

12

On the dual nature of urban planning system and its complexity

Hoblyk A., Suprun P.

Przestrzeń i Forma

|

2016

|

nr 27

111--116

EN

This article presents an analysis of scientific ideas of the followers of the Complexity Theories of Cities and representatives of the Ukrainian urban planning school pertaining to the structure of the urban planning system, its nature and complexity. The dual nature of the urban planning system is explained on the examples using I. Newton’s analog method.

13

Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex function

Antczak T., Jimenez M. A.

Opuscula Mathematica

|

2014

|

Vol. 34, no. 4

665--682

EN

In this paper, we generalize the notion of B-(p, r)-invexity introduced by Antczak in [A class of B-(p; r)-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187–206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove sufficient optimality conditions under the assumptions that the functions constituting them are B-(p, r)-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under B-(p, r)-invexity.

14

Wolfe-type second-order fractional symmetric duality

Jayswal A, Stancu-Minasian I. M., Prasad A. K.

Journal of Applied Analysis

|

2014

|

Vol. 20, nr 2

155-156

EN

In the present paper, we examine duality results for Wolfe-type second-order fractional symmetric dual programs. These duality results are then used to investigate minimax mixed integer symmetric dual fractional programs. We also discuss self-duality results at the end.

15

Rough Set Characterization for 2-circuit Matroid

Wang S., Zhu Q., Zhu W., Min F.

Fundamenta Informaticae

|

2014

|

Vol. 129, nr 4

377--393

EN

Rough sets are efficient to extract rules from information systems. Matroids generalize the linear independency in vector spaces and the cycle in graphs. Specifically, matroids provide well-established platforms for greedy algorithms, while most existing algorithms for many rough set problems including attribute reduction are greedy ones. Therefore, the combination between rough sets and matroids may bring new efficient solutions to those important and difficult problems. In this paper, 2-circuit matroids, abstracted from matroidal characteristics of rough sets, are studied and axiomatized. A matroid is induced by an equivalence relation, and its characteristics including the independent set and duality are represented with rough sets. Based on these rough set representations, this special type of matroid is defined as 2-circuit matroids. Conversely, an equivalence relation is induced by a matroid, and its relationship with the above induction is further investigated. Finally, a number of axioms of the 2-circuit matroid are obtained through rough sets. These interesting and diverse axioms demonstrate the potential for the connection between rough sets and matroids.

16

Generalized α-V-univex functions for multiobjective variational control problems

Sharma S., Choudhury S., Jayswal A.

Control and Cybernetics

|

2014

|

Vol. 43, no. 3

403--420

EN

The purpose of this paper is to introduce a new class of _-V-univex/ generalized _-V-univex functions for a class of multiobjective variational control problems. Moreover, sufficient optimality conditions and Mond-Weir type duality results, associated with the multiobjective variational control problem, are established under aforesaid assumptions.

17

Duality of variable fractional order difference operators and its application in identification

Sierociuk D., Twardy M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2014

|

Vol. 62, nr 4

809--815

EN

The paper presents a number of definitions of variable order difference and discusses duality among some of them. The duality is used to improve the performance of the least squares estimation when applied to variable order difference fractional systems. It turns out, that by appropriate exploitation of duality one can reduce the estimator variance when system identification is carried out.

18

Nondifferentiable (Phi,rho)-type I and generalized (Phi,rho)-type I functions in nonsmooth vector optimization

Antczak T.

Journal of Applied Analysis

|

2013

|

Vol. 19, nr 2

247--270

EN

In this paper, new classes of nondifferentiable generalized invex functions are introduced. Further, nonsmooth vector optimization problems with functions belonging to the introduced classes of (generalized) (Phi,rho)-type I functions are considered. Sufficient optimality conditions and duality results for such classes of nonsmooth vector optimization problems are established. It turns out that the presented results are proved also for such nonconvex vector optimization problems in which not all functions constituting them possess the fundamental property of invexity.

19

Duality in Rough Set Theory Based on the Square of Opposition

Yao Y.

Fundamenta Informaticae

|

2013

|

Vol. 127, nr 1-4

49--64

EN

In rough set theory, one typically considers pairs of dual entities such as a pair of lower and upper approximations, a pair of indiscernibility and discernibility relations, a pair of sets of core and non-useful attributes, and several more. By adopting a framework known as hypercubes of duality, of which the square of opposition is a special case, this paper investigates the role of duality for interpreting fundamental concepts in rough set analysis. The objective is not to introduce new concepts, but to revisit the existing concepts by casting them in a common framework so that we can obtain more insights into an understanding of these concepts and their relationships. We demonstrate that these concepts can, in fact, be defined and explained in a common framework, although they first appear to be very different and have been studied in somewhat isolated ways.

20

Nonconvex minimization related to quadratic double-well energy - approximation by convex problemsenergy – approximation by convex problems

Naniewicz Z., Puchała P.

Control and Cybernetics

|

2012

|

Vol. 41, no. 3

525-543

EN

A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied taking into account minimization of the corresponding integral functional. Such integral, as being not sequentially weakly lower semicontinuous, does not admit classical minimizers. To derive the relaxation formula for the infimum, the appropriate minimizing sequence is constructed. It consists of solutions of some approximating convex problems involving characteristic functions related to the phase energies. The weak limit of this sequence and the weak limit of the sequence of solutions of dual problems combined with the weak-star limits of the characteristic functions related to the phase energies allow to establish the final relaxation formula. It is also shown that infimum can be expressed by the Young measure associated with constructed minimizing sequence. An explicit form of Young measure in some regions of the involved domain is calculated.