The laboratory was established by Prof. A.S. Strekalovsky in 1993 at the Computing Centre of the Irkutsk State University under the name Laboratory of Control and Optimization Problems. In 1997 the laboratory became a part of the Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences and was renamed as the Laboratory of Global Optimization Methods. Nowadays, the laboratory is named after Laboratory for Nonconvex Optimization. Prof. A.S. Strekalovsky has been working as the head of the laboratory since the day of its founding.
The laboratory has extensive contacts with scientific groups from many Institutes and Universities of Moscow, Omsk, Nijnii Novgorod, Saint Petersburgs, Novosibirsk and with foreign researchers from many countries: the USA, Germany, Italy, France, Mongolia, Spain, Norway, Portugal.
Please, see the following paper for a survey of our research ( .pdf).
In recent three decades attention of the specialists involved in solving extremum problems has often been attracted to nonconvex optimization problems [1, 2], which may have a sufficiently large number of local solutions and stationary (critical, say, in the sense of Ferma or Lagrange conditions) points, which are rather far from - even in the aspect of the goal functional - from the global solution, which is so essential from the practical viewpoint. Meanwhile, convex problems, as known from [3]-[5], possess the property that even each local solution turns out to be also global.
Noteworthy, in practice, convex problems occur rather seldom, while there are many examples of convex problems in textbooks [1]-[5]. Furthermore, in applied problems, nonconvex structures most frequently occur in a hidden form. As a consequence, the specialists not always pay attention to their presence and to the nature of their occurrence, as, for example, in problems of hierarchical optimization and optimal control of nonlinear systems. One knows that it is difficult to hope for any success without knowing the structure of the convexity. Note that rather frequently nonconvex structures are generated by convex ones (complementing of the convex set, maximization of the convex function, etc.)[1, 2, 6].
On the other hand, specialists in applied problems do not think about the correctness of direct application of classical methods of optimization in nonconvex problems, while the numerical results are interpreted only in the content aspect, without thinking of the fact that all classical optimization methods (Newtonian ones, methods of conjugate gradients, methods of feasible directions, barrier methods, etc.) converge to the global solution only in convex problems [6]-[7].
At the same time, in nonconvex problems, the direct application of standard methods may have unpredictable consequences [1]-[5], and sometimes may even distract one from the desired solution. So, it is quite natural (but hardly ever grounded) is the reaction of the specialists propagating methods of direct selection - such as the method of branches and bounds (and cuts methods), which, as known, suffer curse of dimension, when the volume of computations grows exponentially side by side with the growth of the problem's dimension [1, 2]. We are sure, there exists also another way of solving nonconvex problems of high dimension (see our publications section).
In the recent two decades, we have managed to construct a theory of global search, which is harmonic from the viewpoint of the theory of optimization and which unexpectedly has turned out to be rather efficient in the aspect of computations, especially for the problems of high dimensions. Necessary and sufficient Global Optimality Conditions (GOCs) for the principal classes of nonconvex problems have turned out to be the kernel of this theory (see below) [6].
On the other hand, we have proposed a family of local search methods (LSMs), which, on the one hand, in some cases develop methods earlier known for the special problems and, on the other hand, this family of LSms represents a joint ensemble of methods, which is harmonic from the viewpoint of GOCs [6, 7, 10, 11].
Meanwhile, the procedures of escape from the stationary or local solutions, which are based on GOCs, are unique and quite efficient even in case of any simplest implementation [6, 7].
The approach elaborated has been tested on a wide field of nonconvex problems (some part of which is represented below). It has demonstrated an unexpected efficiency during the numerical solving problems of high dimension. Note, convex optimization methods are successfully used "inside" the procedures of local and global search proposed.