From September 23 to 26, 2025, the Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine held the XLIX International Scientific Mathematical School (ISMS) “Problems of Computational Optimization”, dedicated to the 95th anniversary of academician V.S. Mikhalevich.
The event was conducted online via the Zoom platform.
The ISMS was organized in accordance with the resolution of the XLVIII International Symposium “Problems of Computational Optimization” (2023) and in line with the plans of the National Academy of Sciences of Ukraine and the Glushkov Institute of Cybernetics of the NAS of Ukraine.
The organizers were:
the Ministry of Education and Science of Ukraine, the National Academy of Sciences of Ukraine, the Glushkov Institute of Cybernetics of the NAS of Ukraine, V.N. Karazin Kharkiv National University, and PJSC “Institute of Information Technologies” (Kharkiv).
During the School, new scientific directions in the field of computational optimization were outlined, and prospects for their further development were discussed.
The lectures presented novel results and practical applications, as well as opportunities for scientific cooperation.
The main scientific focus of the ISMS is the construction of optimal and near-optimal algorithms in terms of time and accuracy, and the development of computer technologies for solving problems of applied and computational mathematics with predefined quality characteristics for precision and performance.
The implementation of these approaches allows reducing computational costs and uncertainty in computer modeling and expanding the class of problems solvable under limited resources.
Special attention was paid to different computational models, the selection of appropriate information operators, refinement of a priori problem information, modern quantum technologies for cryptographic data protection, mathematical methods of artificial intelligence, and other relevant areas.
The School was attended by 80 scientists, including 5 academicians of the NAS of Ukraine, an academician of the Academy of Sciences of Higher Education of Ukraine, an academician of the Academy of Applied Radio Electronics, an academician of the International Academy of Informatics, 7 corresponding members, 43 doctors of sciences, 27 PhDs, 9 postgraduate students, 3 students, and researchers and faculty members from 25 organizations across Ukraine, the United Kingdom, Germany, Poland, Switzerland, and Hungary.
At the opening session, welcoming speeches were delivered by members of the ISMS Program Committee — Academicians of the NAS of Ukraine I.V. Sergienko, O.M. Khimich, and V.K. Zadiraka.
A report on the life and scientific path of Academician V.S. Mikhalevich was presented by PhD in Physics and Mathematics V.M. Kuzmenko.
The Academic Secretary of the ISMS, PhD in Physics and Mathematics I.V. Shvidchenko, informed participants about the composition of the School, the publications issued, and the working schedule.
The participants observed a minute of silence in memory of Academician V.S. Mikhalevich — Director of the Glushkov Institute of Cybernetics of the NAS of Ukraine and Head of the Program Committee of the scientific forums on computational optimization (1982–1994).
Tribute was also paid to long-term participants of previous International Forums.
The ISMS was held within nine thematic sections:
General Theory of Computational Optimization
Approximation and Reconstruction of Functions and Functionals
Digital Signal and Image Processing
Solving Equations
Systems Analysis, Optimization, and Mathematical Programming
Methods of Information Protection
Quantum Computing
Mathematical Methods of Artificial Intelligence
Applied Problems
Each section featured two lectures delivered by leading Ukrainian and international scientists.
 Speaker: Zadiraka V.K., Academician of the National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences, Professor (V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv)Topic: "Elements of the General Theory of Optimal Algorithms" Abstract: The general scheme for estimating the total error of a computational algorithm is presented, the construction of optimal algorithms is described under the conditions of the most complete use of available information about the problem. The reserves of optimization of calculations are considered. |
 Lecturer: Khimich O.M., Academician of the National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences, Professor (V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv)Topic: "High-performance computing" Abstract: Modern approaches to high-performance computing in the context of mathematical modeling of complex processes and systems are presented. Special attention is paid to the use of parallel computing. |
Section 2. Approximation and recovery of functions and functionalities
 Lecturer: Malachivsky P.S., Doctor of Technical Sciences, Professor (Institute of Applied Problems of Mechanics and Mathematics of the Ya. S. Pidstryhach NAS of Ukraine, Lviv)Topic: "Chebyshev approximation of functions of many variables by a nonlinear function of a rational expression" Abstract: The method of constructing the Chebyshev approximation of functions of many variables by an exponent, logarithm and a fixed real power of a rational expression is presented. |
 Lecturer: Nechuyviter O.P., Doctor of Physical and Mathematical Sciences, Professor (Teaching and Scientific Institute "Ukrainian Engineering and Pedagogical Academy" of V.N. Karazin Kharkiv National University, Kharkiv)Topic: "Approximate calculation of double integrals of rapidly oscillating functions of general form using the optimal in order of accuracy cubature formula on the class of differential functions" Abstract: An optimal in order of accuracy cubature formula is given for calculating double integrals of rapidly oscillating functions of general type using Lytvyn information operators on the class of differential functions. |
Section 3. Digital signal and image processing
 Lecturer: Nikolaychuk Ya.M., Academician of the International Academy of Informatics, Doctor of Technical Sciences, Professor (West Ukrainian National University, Ternopil)Topic: "High-performance computing in the system of residual classes" Abstract: The mathematical foundations of data encoding and performing modular operations in the system of residual classes are presented. The mathematical transformations of the system of orthogonal harmonic functions of the Fourier number-theoretic basis are investigated. |
 Lecturer: Semenov V.Yu., Doctor of Physical and Mathematical Sciences, Senior Researcher (Kyiv Academic University, LLC "Delta SPE", Kyiv)Topic: "Application of Machine Learning Methods to Some Problems of Digital Signal Processing in Telecommunications Problems" Abstract: Four machine learning methods are considered: multinomial regression, nearest neighbor method, Gaussian mixtures and convolutional neural network. Experiments showed that the highest accuracy (99%) was provided by the convolutional neural network. |
Section 4. Solving equations
 Lecturer: Nedashkovsky M.O., Doctor of Physical and Mathematical Sciences, Professor (Ivan Franko National University of Lviv, Lviv)Topic: "Solution of matrix polynomial equations" Abstract: The method of solving matrix polynomial equations of arbitrary order with matrix and vector unknowns is demonstrated. An approach to calculating solution tuples based on the theory of branched continued fractions is presented. The application of such equations in optimization of control systems and mathematical economics is indicated. |
 Lecturer: Popov O.V., Doctor of Physical and Mathematical Sciences, Senior Researcher (V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv)Topic: "Parallel Computing in Mathematical Modeling" Abstract: The issue of improving the quality and efficiency of mathematical modeling, the use of large-scale models, and ensuring the reliability of results taking into account the errors of the initial data is considered. |
Section 5. Systems analysis, optimization, mathematical programming
 Lecturer: Stetsyuk P.I., Corresponding Member of the NAS of Ukraine, Doctor of Physical and Mathematical Sciences, Senior Researcher (V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv)Topic: “Scientific Heritage of Shor N.Z.” Abstract: A review of the scientific heritage of Academician N.Z. Shor is presented. The main ideas are considered: the method of sequential analysis of variants, the subgradient method, the use of linear non-orthogonal transformations to improve the conditionality of ravine functions, as well as the dual approach in non-convex quadratic models. Examples of the implementation of these ideas in the methods and algorithms of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine are given. |
 Lecturer: Semenov V.V., Doctor of Physical and Mathematical Sciences (Taras Shevchenko National University of Kyiv, Kyiv)Topic: "Operator Extrapolation Method for Variational Inequalities and Its Applications" Abstract: New iterative algorithms for solving monotone variational inequalities in Hilbert space are presented. |
Section 6. Information protection methods
 Lecturer: Gorbenko I.D., Academician of the Academy of Sciences of Applied Radio Electronics, Doctor of Technical Sciences (Kharkiv National University named after V.N. Karazin, Kharkiv)Topic: "National and International Post-Quantum Standards of Asymmetric Transformations" Abstract: The current state and prospects of standardization of post-quantum algorithms of asymmetric transformations at the national and international levels are analyzed. An overview of the NIST competition for standardization of post-quantum key encapsulation and electronic signature mechanisms is provided. |
 Lecturer: Kudin A.M., Chief Expert of the Information Security Department of the Security Department (National Bank of Ukraine), Corresponding Member of the NAS of Ukraine, Doctor of Technical Sciences, Senior Researcher (National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv)Topic: "Application of the General Theory of Optimal Algorithms in Cryptography, Steganography and Blockchain Technologies" Abstract: It is shown that the analysis and synthesis of one-way functions and functions with a loophole are the basis for assessing the stability and construction of cryptographic transformations, steganographic systems and blockchain consensus protocols. |
Section 7. Quantum Computing
 Lecturer: Vasiliu E.V., Doctor of Technical Sciences (State University of Intellectual Technologies and Communications, Odessa)Topic: "Modern Quantum Technologies of Cryptographic Information Protection" Abstract: An overview of modern quantum technologies of information protection is presented: protocols of quantum key distribution, quantum direct secure communication and quantum secret sharing. |
 Lecturer: Fesenko A.V., Candidate of Physical and Mathematical Sciences (Physical and Technical Institute of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv)Topic: "Use of combined post-quantum digital signature schemes and key encapsulation mechanisms" Abstract: Combined digital signature schemes and combined key encapsulation mechanisms are considered to improve the security of information systems. |
Section 8. Mathematical methods of artificial intelligence
 Lecturer: Zgurovsky M.Z., Academician of the National Academy of Sciences of Ukraine, Doctor of Technical Sciences, Professor (Educational and Scientific Complex "Institute of Applied Systems Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" of the National Academy of Sciences and the Ministry of Education and Science of Ukraine, Kyiv)Topic: "Global Trends in Artificial Intelligence: Opportunities and Challenges for Ukraine" Abstract: An overview of current trends in the development of artificial intelligence is provided, in particular, new opportunities and challenges facing Ukraine in this area. |
 Lecturer: Letichevsky O.O., Doctor of Physical and Mathematical Sciences, Senior Researcher (V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv)Topic: "Neuro-symbolic doubles of systems and their use" Abstract: The combination of three technologies - artificial intelligence, algebraic approach and formal methods in the creation of neuro-symbolic digital doubles of systems is considered. |
Section 9. Applied Problems
 Lecturer: Bomba A.Ya., Doctor of Technical Sciences, Professor (National University of Water Management and Environmental Management, Rivne)Topic: "Methods of complex analysis of forecasting controlled movements of surface and filtration waters" Abstract: An approach to modeling ideal flow in an aquatic environment limited by flow lines and equipotential surfaces, in particular in water bodies with tributaries, is considered. |
 Lecturer: Shevchuk B.M., Doctor of Technical Sciences, Senior Researcher (V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv)Topic: "Methods, algorithms and means of remote long-term monitoring of the safety of people and their property" Abstract: The methodological and algorithmic foundations of the functioning of terminal, local-regional and global wireless networks for long-term monitoring of the safety of people and their property are presented. |
Along with the lectures, the participants actively exchanged experiences and participated in discussions.
At the final meeting, a general discussion was held dedicated to the school's topics and the reports heard. It was noted that the lectures had a high scientific level, contained new results and outlined promising research directions.
The Program Committee highly appreciated the level of organizational work, careful preparation of the school's topics, the creation of the official website http://iscopt.com.ua/ and the publication of lecture materials.
The school became an important basis for young scientists and specialists who have recently joined the issues of the event.
Following the discussion, the following decision was unanimously adopted:
I. Concluding part
- To recognize that the main goal of the MNMSH, to familiarize specialists with new results of research on the accuracy and computational complexity of algorithms, as well as solving typical classes of problems in computational, applied and discrete mathematics, has been achieved.
- To introduce a new section “Mathematical Methods of Artificial Intelligence” and note its relevance, which is confirmed by the high interest of the participants.
- To note the high scientific level of the lectures and their relevance.
- To state that the results of research on optimization of calculations are actively implemented in other branches of science to solve complex scientific, technical and applied problems.
II. Propositional part
- Conducting scientific forums:
- To recognize the expediency of holding scientific forums on optimization of calculations at least once every two years.
- The next forum – the International Scientific Symposium “Issues of Optimization of Calculations (POO-L)” – to be held in September 2027.
- Cooperation:
- To initiate in-depth cooperation between the NAS of Ukraine, higher education institutions and foreign universities in order to attract young scientists to scientific forums.
- Reports and research areas:
- Recommend an increase in the number of reports devoted to the use of supercomputers, quantum computers and specialized processors for AI.
- Increase attention to the use of artificial intelligence methods to improve the quality of algorithms for solving complex problems.
- Publications and reporting:
- Post the school's report materials on the website of the International Scientific Forums (http://iscopt.com.ua/).
- Publish information about the MNMSH on the websites of the Presidium of the NAS of Ukraine, the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine and in the journal "Cybernetics and System Analysis".
- Acknowledgements:
- Express gratitude to the Organizing Committee for the high level of organization and conduct of the school.
The International Scientific Mathematical School "Questions of Computational Optimization" confirmed its role as a leading platform for the development of scientific research in the field of computational optimization.