Preface to the special issue

Abstract

This Special Issue of Optimization Methods and Software is devoted to the International Conference ‘Mathematical Optimization Theory and Operations Research’ (MOTOR 2019), held near Ekaterinburg city, Russia, on 8–12 July 2019. The conferences of MOTOR series are descendants of four well-known international and all-Russian conferences, which were held in Ural, Siberia, and the Far East for several decades. The talks presented at these conferences are frequently published in several special issues of well-known journals. To fulfil the standard number of pages per issue, some regular papers were added to this journal issue after the following three papers were originally submitted to the special issue. The paper ‘Cooperative Differential Games with Continuous Updating Using Hamil-ton–Jacobi–Bellman equation‘ by O. Petrosian, A. Tur, Z. Wang, H. Gao investigates cooperative differential games with structures defined for a closed time interval with a fixed duration. The problem of cooperative players’ behaviour is considered. This paper contains a very nice introduction and theoretical results as well as an illustrative example with a model of non-renewable resource extraction. Dynamic Programming for Travelling Salesman with Precedence Constraints: Parallel Morin–Marsten bounding’ implement a parallel Morin–Marsten Branch-and-Bound Scheme for Dynamic Programming and test it on conventional and bottleneck formulations of the Travelling Salesman with Precedence Constraints, using the benchmark instances from TSPLIB. In the experiment, the parallel scheme to scale well with the number of processors and showed significant memory savings, compared to the non-bounded dynamic programming, especially on the large-scale instances. Variational and methods for solving optimization problems, saddle point problems and variational inequalities are proposed. Smooth and nonsmooth cases are considered. This paper provides sufficient theoretical justification and quite comprehensive numerical testing results.