This work presents lines of investigation and scientific achievements of the Ukrainian school of optimization theory and adjacent disciplines. These include the development of approaches to mathematical theories, methodologies, methods, and application systems for the solution of applied problems in economy, finances, energy saving, agriculture, biology, genetics, environmental protection, hardware and software engineering, information protection, decision making, pattern recognition, self-adapting control of complicated objects, personnel training, etc. The methods developed include sequential analysis of variants, nondifferential optimization, stochastic optimization, discrete optimization, mathematical modeling, econometric modeling, solution of extremum problems on graphs, construction of discrete images and combinatorial recognition, etc. Some of these methods became well known in the world's mathematical community and are now known as classic methods.

Preface.- 1. Science Was the Meaning of His Life.- 2. Optimization Methods and Their Efficient Use.- 3. Mathematical Modeling and Analysis of Complex Processes on Supercomputer Systems.- 4. Problems of Modeling and Analysis of Processes in Economic Cybernetics.- 5. Problems of Solving Complicated Combinatorial Problems.- Afterward.- References.- Index.

Sergienko, Ivan V., D. PM. S. Born in 1936. Recipient of the State Prize for Science and Technology in 1972. Corresponding member since 1978. Recipient of the SSSR State Prize in 1981. Awarded the V. M. Glushkov Prize for Cybernetics, Computer Machine and Systems Theory in 1986. Elected an academician in 1988.