This issue is dedicated to the International Conference on Operations Research and Optimization (ORO2011) which was held at the School of Mathematics, IPM, Tehran, Iran on 26–28 January 2011. The organizers of the conference were the Institute for Research in Fundamental Sciences (IPM) and School of Mathematics, Statistics and Computer Science, University of Tehran (UT).
IPM is an Iranian institute which was found in 1989 under the name ‘Institute for Studies in Theoretical Physics and Mathematics (IPM)’ and its goal is the advancement of research and innovation in theoretical physics and mathematics. The main activity of the IPM is in direction of promoting the culture of research all across the country.
UT is the oldest and largest university in Iran. It is the best Iranian university in international university rankings and is known as the symbol of higher education in Iran. School of Mathematics, Statistics and Computer Science of UT is the oldest higher education centre for mathematics in Iran.
The aim of ORO conference is to bring together researchers and scientists from all over the world to discuss theoretical and applied aspects of ORO. The conference also aims to construct an atmosphere of cooperation between national institutions as well as international ones which are active in the area of ORO and related disciplines. There were rigorous plenary talks by seven invited speakers in ORO2011. Moreover, there were 40 contributed talks, selected from among 250 submissions. Some selected high-quality papers as well as some invited papers have been considered for publication in this issue, after completing the standard review process. In the following, we review the accepted papers briefly.
In the first paper, Mahdavi-Amiri and Ansari dealt with a structured algorithm for solving constrained non-linear least-square problems which makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians. The authors discussed relevant results on global convergence and computational benefits.
The authors of the second paper are Alizadeh and Hadjisavvas, who extended the definition of monotone bifunctions. In the new definition, the Fitzpatrick transform of a maximal monotone bifunction is introduced so as to correspond exactly to the Fitzpatrick function of a maximal monotone operator in case the bifunction is constructed starting from the operator.
Ghaznavi-ghosoni et al. dealt with the concept of weak/strong/proper approximate solution for multiobjective optimization problems in the next paper. They provided some necessary and sufficient optimality conditions, via standard scalarization approaches. The results obtained by the modified constrained method and the modified weighted Tchebycheff method are general, and any convexity assumption is not required.
The authors of the fourth paper are Ansari and Rezaei. They established some properties of pseudoinvex functions, defined by means of limiting subdifferential. Furthermore, they studied the equivalence between vector variational-like inequalities involving limiting subdifferential and vector optimization problems.
The fifth paper, presented by Popovici and Rocca, is devoted to studying the structure of solution sets within a special class of generalized Stampacchia-type vector variational inequalities. The authors showed that, similar to multicriteria optimization problems, under appropriate assumptions, the (weak) solutions of these vector variational inequalities can be recovered by solving a family of weighted scalar variational inequalities.
New second-order optimality conditions and new multiplier rules in set-valued optimization via asymptotic derivatives have been provided by Khan and Tammer in the sixth paper. They extended the well-known Dubovitskii–Milyutin approach to set-valued optimization. They also give optimality conditions in terms of a disjunction of certain cones in the image space.
In the seventh article, Bagirov et al. studied main properties of the hyperbolic smoothing functions and gave an approach for solving finite minimax problems, based on the use of these functions. Furthermore, they proposed an algorithm for solving the finite minimax problem. They completed the paper by presenting some numerical experiments with well-known test problems and comparing the proposed algorithm with some current ones.
Golestani and Nobakhtian considered a non-smooth multiobjective programming problem with inequality and set constraints in the next paper. They extended some constraint qualifications, and derived strong Kuhn–Tucker necessary optimality conditions utilizing the notion of convexificator.
In ninth paper, Bidabadi and Mahdavi-Amiri presented an exact penalty approach for solving constrained least-square problems, when the projected structured Hessian is approximated by a projected version of the structured BFGS formula. They discussed the convergence and numerical benefits of the given algorithm.
Oveisiha and Zafarani obtained some properties for K–preinvex set-valued maps in terms of normal subdifferential in the tenth paper. They provided some sufficient conditions for the existence of super minimal points and some necessary optimality conditions for a general kind of super efficiency.
The last paper is by Daryaei and Mohebi in which the theory of extended real-valued ICR functions defined on an ordered topological vector space X has been developed. A characterization of non-positive ICR functions was given and abstract convexity of this class of functions was examined. The authors also investigated polar functions and subdifferential of these functions and characterized abstract convexity, support set and subdifferential of extended real-valued ICR functions.