Abstract: We propose an approach to feedback control for both nonlinear objects with lumped parameters and point sources of objects with distributed parameters. The approach lies in the fact that the entire set of possible phase states of an object is divided into a finite number of zones (subsets), and the synthesized controls are determined not by the measured state values themselves, but by the zonal values of the zone parameters to which belong the current measured object states. We have obtained necessary optimality conditions for the zonal values of the feedback parameters, carried out computational (computer) experiments on some test problems of feedback control both for objects with lumped parameters and for distributed parameters.

Abstract: Depth functions have been exploited in supervised learning since years. Given that the depth of a point is somehow a distribution-free measure of its distance from the center of a distribution, their use in supervised learning arose naturally and it has seen a certain degree of success. Particularly, DD-classifers and their extensions have been extensively studied and applied in many applied fields and statistical settings. What has not been investigated so far is their use within a semi-supervised learning framework. That is, in case some labeled data are available along with some unlabeled data within the same training set. A case which arises in many applications and where it has been proved that combining information from labeled and unlabeled data can improve the overall performance of a classifier. For this reason, this work aims at introducing semi-supervised learning techniques in association with DD-classifiers and at investigating to what extent such technique is able to improve DD-classifier performances. Performances will be evaluated by means of an extensive simulation study and illustrated on some real data sets.

Abstract: The goal of this talk is to study convergence of approximation methods for quasi-variational inequalities with the moving set. First, we propose the extragradient dynamical system and under strong monotonicity we show strong convergence with exponential rate of generated trajectory to the unique solution of quasi-variational inequality. Further, the explicit time discretization of this dynamical system leads to an extragradient algorithm with relaxation parameters. We prove the convergence of the generated iterative sequence to the unique solution of the quasi-variational inequality and derive the linear convergence rate under strong monotonicity.

Abstract: The MIP/LP solvers are primarily developed by the operations research community while SAT/SMT solvers are primarily developed by the computer science community. However, these problems are closely related with each other. In recent years, there have been many attempts to combine the algorithmic techniques of both sides to develop better solvers. In this talk, I will discuss about these and our attempts and try to provide a unified perspective and framework.

Abstract: Distribution systems face significant changes due to the growing number of distributed and variable energy generation resources and the smart grid implementation. The traditional design paradigm can no longer meet the need for greater resilience, power quality, and customer participation. On the other hand, smart grid implementation brings a large amount of data that can be used to better plan a distribution system. Growing energy demand and limited investment capital make distribution system planners look to these advances in smart grid technology to identify new approaches to achieve load reliability. When planning a distribution system, the main goal is to meet the most economically and reliably timed demand growth. The planning methodology must ensure that every opportunity for savings or power quality improvement is exploited. This is not a straightforward task, even in traditional systems, since the distribution networks are usually large in extension, with a large amount of data to be analyzed. In addition, new regulations from authorities and the modernization of power systems highlight the importance of a constant update and improvement of methodologies and planning techniques. The ongoing changes bring enormous opportunities and challenges to traditional and new players requiring huge planning and operation methods changes. With more and innovative players entering the sector, artificial intelligence-based approaches can be the key to dealing with the new challenges and ensuring the systems and the respective players' sustainability, both in economic and environmental terms. The drive to make utilities more efficient through AI, machine learning, and data science has resulted in major benefits for every actor in the energy sector, including generators, distributors, the environment, taxpayers, and consumers.

Abstract: When designing AI tools or machine-learning models, one must make multiple choices: which approach should be used, which structure of model is more appropriate for the problem in hand and which settings and parameters must be applied. All of these choices are mathematically reduced to some kind of optimization problem. In fact, one has to solve multi-criteria multi-dimensional multi-scale “black box” optimization problems with algorithmically-given objectives and/or constraints. Bio-inspired algorithms, e.g. evolutionary algorithms (EAs), could be used for solving the described problems. However, the effectiveness and efficiency of EAs depends essentially on the choice of their settings and the tuning of their parameters, which is a separate and very complicated decision-making problem. An EA with appropriate settings and parameters can be very effective, but in the opposite case, this algorithm can fail. Moreover, such a useful property of EAs as their universality (their independence from the properties of the problem), which allows them to be used in solving the widest class of optimization problems, means that it is impossible to use properties of problems convenient for optimization (such as convexity, monotony and unimodality) in cases where such properties exist in the problem being solved. The approach that will be discussed in the lecture allows us to simplify the use of EAs and other bio-inspired algorithms by means of the self-configuration, coevolution and hybridization of EAs with problem-specific algorithms. Details of the approach will be described, and examples of approach deployment in the automated design of AI-tools will be given.

Abstract: In this talk, a recent computational methodology is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework. It is based on the principle ‘The part is less than the whole’ applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The methodology uses as a computational device the Infinity Computer (a new kind of supercomputer patented in several countries) working numerically with infinite and infinitesimal numbers that can be written in a positional system with an infinite radix. On a number of examples (numerical differentiation, divergent series, ordinary differential equations, fractals, set theory, etc.) it is shown that the new approach can be useful from both theoretical and computational points of view. The main attention is dedicated to applications in optimization (local, global, and multi-objective). The accuracy of the obtained results is continuously compared with results obtained by traditional tools used to work with mathematical objects involving infinity. The Infinity Calculator working with infinities and infinitesimals numerically is shown during the lecture.

Abstract: The developed countries made a transition from intensive to extensive growth in 1980s, that led to goods and services range extension. Related changes in the technologies during the economic globalization caused supply chains sophistication and complex production network development in local and global economies. The problem of sustainable development of regional economies while supply chains was localized raised due to latest pandemic and sanction economic shocks. Proper tools are needed to describe modern production networks taking into account the substitution of inputs. Traditional interindustry balance method based on the Leontief linear model and nonnegative matrices theory should not be used due to its base assumption of the constancy of direct requirement coefficients in a supply network. Modern methods demand new mathematical tools that reflect substitution of inputs in complex production networks. Tools presented by authors developed on the results of the analysis of the resource allocation problem with positively homogeneous neoclassical production functions and the dual problem which solutions are the price indexes of intermediate inputs. The way of problem studying is based on the construction of the Young dual transform for equilibrium price indexes. It is proved that in the case of CES technologies with constant elasticity of substitution (Cobb-Douglas in particular) resource allocation problem has an explicit solution. In this case the comparative statics method based on the official national accounts statistics is developed by authors. Method allows in a middle-term to forecast intersectoral links under given scenarios of the internal or external shocks taking into account the substitution of inputs. The point of the method is solving the inverse problem of nonlinear balance identification and further verification of the model on the base of the official input-output tables statistics. By that the elasticities of substitution of intermediate inputs are the verification parameters of the model. The method was successfully tested on the input-output tables statistics of Russia and Kazakhstan. Applications to the analysis of the intersectoral links of several countries with different levels of market relations maturity demonstrated that in the case of decentralized economy the nonlinear balance with Cobb-Douglas production functions gives more precise forecast than traditional linear Leontief model approach.

Abstract: The topic of our lecture is a class of recurrent neural networks (RNN) dedicated to find- ing zeros of equations or minimizing nonlinear functions. Optimization RNN models are divided into two global classes: Gradient Neural Networks (GNN) and Zhang Neural Net- works (ZNN). GNN models are aimed at solving time-invariant problems, while ZNN models are able to solve time-varying problems. The design of GNN and ZNN models arises from the choice of an appropriate error function. ZNN dynamics is a certain dynamical system whose states evolve over a state space continuously based on the time derivative of the error function. Some new error functions resulting from nonlinear gradient-descent and quasi- Newton optimization methods are presented. A modification of ZNN dynamical evolution based on higher-order hyperpower iterative methods is described. We discuss the prob- lems of non-differentiability and division by zero (DBZ) which appear relatively frequently in time-varying dynamical systems. The GNN design is defined as a movement along the negative gradient of the Frobenius norm of the error function inside the time interval. Mod- ifications of the GNN flow based on gradient-descent and conjugate-gradient optimization methods are considered. In general, dynamical systems are defined as continuous-time analogies of known nonlinear optimization algorithms, such as the class of gradient-descent algorithms or various quasi-Newton method for solving nonlinear optimization problems. The convergence of various modified dynamical systems aimed to solving time-varying ma- trix equations are investigated.

Abstract: This lecture presents a short overview of iterative solution methods of Fejér type for the well-known quadratic constrained optimization problem, which were introduced and widely studied by acad. I.I. Eremin - the founder of the Ural mathematical programming school. Along with common quadratic programs, we consider several variants of the basic problem, which have numerous applications. We point attention to some special settings of the problem in question including metric projections, linear programming, etc., which are of separate interest. Fejér-type methods adopt interest of specialists on numerical optimization, since, along with convergence, one can prove conditions of their stability to small perturbations of input data. Thus, these methods induce self-regularizing algorithms, unlike some well-known primal numerical optimization techniques (see, e.g. the classic book by C.T.Lawson, R.J.Hansen, 1995).

Abstract: This talk will shine a spotlight on the challenges software developer faces when applying Operations Research methods in the development and implementation of software solutions. Typically, large transportation companies consist of a number of branches, including production (those who own vehicles), sales (those who sell company services and must know what prices will be set for each individual type of vehicle and each destination), and marketing (those who manage demand by setting up special offers and discounts). The process of operations planning for different branches is interconnected. As a result, the company needs a planning system on both the department and global levels. Planning is required over different time horizons, interdepartmental planning often has a greater planning horizon. The development of these systems has a multitude of complex requirements. This talk will touch upon the implementation of a few systems, one of which—last-mile planning is a multi-depot vehicle routing problem with time windows. Another problem that is going to be discussed is assigning a vehicle to a transportation request, which in an essence is the assignment problem. Implementation steps, infrastructure, and algorithm requirements will also be explored. The challenges of implementation are important to mention since the automated planning process is different from what end-users are used to, so a level of trust has to be achieved. Finally, we will talk about possible ways to further the progress of implementation of these technologies into a real-world context, for example, by means of open source projects.