This special issue of the journal Optimization is brought out on the occasion of International Conference on Recent Advances in Optimization Theory and Applications (RAOTA-2016). The conference was jointly organized by the Mathematical Programming Group (MPG), Delhi, Department of Operational Research, University of Delhi and Department of Mathematics, University of Delhi during 30–31 January 2016, at the Satyakam Bhawan, University of Delhi, North Campus, Delhi, India. It was dedicated to Late Professor Dr M. C. Puri, a pioneer member of the MPG, Delhi. The conference was focused on new developments in theoretical and computational techniques of optimization and related applications from diverse areas.
The special issue devoted to RAOTA-2016 contains selected refereed papers submitted to the journal in response to the call for papers of the special issue. The finally accepted 12 papers cover wide range of optimization topics including set optimization problem, set-valued optimization problem, programming problems involving linear and quadratic functions, vector optimization and vector variational inequalities using convexificators, minimax programming problem with mathematical constraints, and non-smooth convex vector optimization problem. Furthermore, the papers also cover wide range of optimization applications such as vehicle routing problem applied to garbage collection, integrated multi-criteria optimization method for COTS evaluation and selection, twin vector support machine models-based regression, complex project selection problem, ranking method for bi-objective quadratic integer programme, and optimal portfolio execution problem with cointegration behaviour. The papers are arranged in two broad categories namely, theoretical advancements and new methodological developments.
The first paper, entitled ‘Characterizations of set order relations and constrained set optimization problems via oriented distance function’, by Chen, Ansari and Yao, focuses on deriving necessary and sufficient optimality conditions for optimal solution of different types of constrained set optimization problem with respect to the set order relations.
The second paper, entitled ‘Necessary optimality conditions for minimax programming problems with mathematical constraints’, by Bao, Gupta and Khanh, presents necessary optimality conditions in terms of upper and/or lower subdifferentials for minimax optimization problems in the setting of non-differentiable and non-Lipschitz functions in the Asplund spaces along with the necessary optimality conditions in the fuzzy form.
The third paper, entitled ‘A unifying approach to solve a class of rank-three programs involving linear and quadratic functions’, by Cambini and Sodini, presents optimal level solutions method in a new unifying framework and is used to solve a class of low-rank programmes involving linear and quadratic functions and having a polyhedral feasible region.
The fourth paper, entitled ‘Approximate solutions and scalarization in set-valued optimization’, by Dhingra and Lalitha, presents certain notions of approximate weak efficient solutions for a set-valued optimization problem based on vector and set criteria approaches.
The fifth paper, entitled ‘Gap functions and error bounds for nonsmooth convex vector optimization problem’, by Dutta, Kesarwani and Gupta, develop gap functions and error bounds for a non-smooth convex vector optimization problem.
The sixth paper, entitled ‘On vector optimization problems and vector variational inequalities using convexificators’, by Laha and Mishra, present some results which exhibit an application of convexificators in vector optimization problems and vector variational inequalities involving locally Lipschitz functions.
The seventh paper, entitled ‘Optimizing garbage collection vehicle routing problem with alternative fuel-powered vehicles’, by Gajpal, Abdulkader, Zhang and Appadoo, presents mathematical formulation and solution approaches for the garbage collection problem in which alternative fuel-powered vehicles with multiple compartments are used to collect the garbage.
The eighth paper, entitled ‘Optimizing project selection: a perspective from resource constraints’, by Zhao and Huang, presents a new project selection model and solution method from the perspective of complex resource constraints wherein the resources are divided into non-renewable and renewable categories, and some resources of the two categories can both be shared by different projects.
The ninth paper, entitled ‘Multi-criteria optimization model integrated with AHP for evaluation and selection of COTS components’, by Verma and Mehlawat, deals with COTS evaluation and selection for developing a modular software system under single application development task considering both quantitative and qualitative criteria, which fulfils specific needs of a software system.
The 10th paper, entitled ‘L1-norm twin support vector machine based regression’, by Rastogi, Anand and Chandra, present two variants of L1-norm twin support vector machine-based regression models which are robust, efficient and own better generalization ability.
The 11th paper, entitled ‘A ranking algorithm for bi-objective quadratic fractional integer programming problems’, by Sharma, Dahiya and Verma, presents an algorithm that uses ε-scalarization technique and a ranking approach of the integer feasible solution to find all non-dominated points of a bi-objective quadratic fractional integer programming problem.
The 12th paper, entitled ‘Optimal portfolio execution under cointegrated vector autoregressive systems’, by Singh, proposes an optimal portfolio execution problem as a quadratic programming problem under price model which exhibits cointegration behaviour.
We sincerely thank all the authors and referees for their efforts in bringing quality publications following high publication standards of the journal Optimization.
We are extremely thankful to Dr Rosalind Elster and Dr Elisabeth Anna Sophia Köbis, Managing Editors, for their immense help and extremely efficient handling of the manuscripts submitted to our special issue. Both of them have been great support throughout the refereeing process.
Martin-Luther-Universität Halle-Wittenberg, GermanyPankaj Gupta
Department of Operational Research, University of Delhi, Delhi, India
[email protected]