Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
Optimality conditions for approximate solutions of vector optimization problems with variable ordering structures
5
23
EN
B.
Soleimani
Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Theodor-Lieser Str. 5, 06120 Halle, Germany.
behnam.soleimani@mathematik.uni-halle.de
C.
Tammer
Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Theodor-Lieser Str. 5, 06120 Halle, Germany.
christiane.tammer@mathematik.uni-halle.de
We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces. Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems. Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimization problems with variable ordering structures applying nonlinear separating functionals and Ekeland's variational principle.
Nonconvex vector optimization,variable ordering structure,Ekeland's variational principle,optimality conditions
http://bims.iranjournals.ir/article_885.html
http://bims.iranjournals.ir/article_885_c784a05612ed4dd1924879eb1e344219.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
Convergence in a sequential two stages decision making process
25
29
EN
J.-E.
Martinez-Legaz
Departament
d'Economia i d'Historia Economica, Universitat Autonoma de
Barcelona, 08193 Bellaterra, and Barcelona Graduate School of Mathematics (BGSMath), BARCELONA, Spain.
juanenrique.martinez.legaz@uab.cat
A.
Soubeyran
Aix-Marseille University (Aix-Marseille School of Economics) CNRS & EHESS, Chateau Lafarge, route des Milles, 13290 Les Milles, France.
antoine.soubeyran@univ-amu.fr
We analyze a sequential decision making process, in which at each step the decision is made in two stages. In the rst stage a partially optimal action is chosen, which allows the decision maker to learn how to improve it under the new environment. We show how inertia (cost of changing) may lead the process to converge to a routine where no further changes are made. We illustrate our scheme with some economic models.
sequential decision making,costs to change,convergence
http://bims.iranjournals.ir/article_891.html
http://bims.iranjournals.ir/article_891_aa887782f9e8dec28eb98d0f4096894b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
Maximal elements of sub-topical functions with applications to global optimization
31
41
EN
A. R.
Doagooei
Department of Applied Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran.
doagooei@uk.ac.ir
We study the support sets of sub-topical functions and investigate their maximal elements in order to establish a necessary and sufficient condition for the global minimum of the difference of two sub-topical functions.
Global optimization,abstract convexity,sub-topical functions,Toland-Singer formula,support set,subdifferential
http://bims.iranjournals.ir/article_886.html
http://bims.iranjournals.ir/article_886_4fe91887a3d2b52c52e5616a296a4306.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
First step immersion in interval linear programming with linear dependencies
43
53
EN
M.
Hladík
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University in Prague, Malostranske Nam. 25, 11800, Prague, Czech Republic.
hladik@kam.mff.cuni.cz
M.
Černý
Department of Econometrics, University of Economics, n'am. W. Churchilla 4, 13067, Prague, Czech Republic.
cernym@vse.cz
We consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals. Contrary to classical models, where parameters can attain any value from the interval domains independently, we study problems with linear dependencies between the parameters. We present a class of problems that are easily solved by reduction to the classical case. In contrast, we also show a class of problems with very simple dependencies, which appear to be hard to deal with. We also point out some interesting open problems.
Linear programming,interval analysis,linear dependencies
http://bims.iranjournals.ir/article_887.html
http://bims.iranjournals.ir/article_887_4300ceea6463c7bf9f165fe17ce6a1be.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
An improved infeasible interior-point method for symmetric cone linear complementarity problem
55
66
EN
N.
Mahdavi-Amiri
Faculty of Mathematical Sciences, Sharif
University of Technology, Tehran, Iran.
nezamm@sharif.edu
B.
Kheirfam
Azarbaijan Shahid Madani University, Tabriz, Iran.
b.kheirfam@azaruniv.edu
We present an improved version of a full Nesterov-Todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (Bull. Iranian Math. Soc., 40(3), 541-564, (2014)). In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new algorithm demands less work in each iteration and admits a simple analysis of complexity bound. The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.
Linear complementarity problem,infeasible interior-point method,symmetric cones,polynomial complexity
http://bims.iranjournals.ir/article_888.html
http://bims.iranjournals.ir/article_888_0bb2cab455dc1ea47c66760ccbcc507d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
Solving multiobjective linear programming problems using ball center of polytopes
67
88
EN
M. A.
Yaghoobi
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
yaghoobi@uk.ac.ir
A.
H. Dehmiry
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
dehmiry@mail.vru.ac.ir
Here, we aim to develop a new algorithm for solving a multiobjective linear programming problem. The algorithm is to obtain a solution which approximately meets the decision maker's preferences. It is proved that the proposed algorithm always converges to a weak efficient solution and at times converges to an efficient solution. Numerical examples and a simulation study are used to illustrate the performance of the proposed algorithm.
Multiobjective linear programming,Eficiency,Polytope,Ball center of a polytope,Target value
http://bims.iranjournals.ir/article_889.html
http://bims.iranjournals.ir/article_889_04ae0492e69eaee30394f8792924760f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
Issue 7 (Special Issue)
2016
12
18
Restricting the parameter set of the Pascoletti-Serafini scalarization
89
112
EN
K.
Khaledian
Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424,
Hafez Ave, 15914, Tehran, Iran
khaledian.k@aut.ac.ir
A common approach to determine efficient solutions of a multiple objective optimization problem is reformulating it to a parameter dependent scalar optimization problem. This reformulation is called scalarization approach. Here, a well-known scalarization approach named Pascoletti-Serafini scalarization is considered. First, some difficulties of this scalarization are discussed and then removed by restricting the parameter set. A method is presented to convert a space ordered by a specific ordering cone to an equivalent space ordered by the natural ordering cone. Utilizing the presented conversion, all confirmed results and theorems for multiple objective optimization problems ordered by the natural ordering cone can be extended to multiple objective optimization problems ordered by specific ordering cones.
Multiple objective optimization,Pascoletti-Serafini scalarization,ordering cone,parameter set restriction,convexification
http://bims.iranjournals.ir/article_890.html
http://bims.iranjournals.ir/article_890_cf164ddd32e9f539c5e38f02ae33a0bf.pdf