Laboratory of models and methods of discrete optimization

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Laboratory	Laboratory of models and methods of discrete optimization
Phone	(+994 12) 539-35-32
Head of laboratory	Mamedov Knyaz Shiraslan Doctor of Mathematics, Professor
Main research areas	Investigation of problems of integer programming of various classes, development of new solution methods, development of appropriate application software packages.
Main scientific achievements	- Solution to the problem of disaggregation of the integral equation. (This problem was posed by US mathematicians and remained unsolved for 30 years); - The criteria have been given in the form of a sufficient condition for finding the small area that provides the optimal solution of the integer knapsack problem and the integer programming problem, and new methods of their solution have been proposed; - A mathematical model has been built and a method has been given for solving the problem of optimal placement and connection of offshore oil and gas platforms; - The criterion that allows minimizing the range of variation of the unknowns in the mixed-integer knapsack problem has been given, and a method for its effective solution has been developed; - Methods of polynomial time complexity for the construction of suboptimal solutions to the problem of Boolean and integer programming have been developed; - A majorant Lagrange-type function has been constructed for problems of Boolean and integer programming and algorithms for its minimization have been developed; - A method has been proposed for finding a smaller region in a given domain, which provides an optimal solution to the problem of mixed-integer programming; - The concepts of guaranteed solution, guaranteed suboptimal solution of problems of Boolean and integer programming have been given, and methods for finding them have been proposed; - The concepts of optimistic, pessimistic, suboptimistic and subpessimistic solutions for the problem of Boolean programming with integer interval data have been given, algorithms for constructing optimistic, pessimistic, suboptimistic and subpessimistic solutions have been developed; - New approximate solution methods that have certain values for various classes of interval mixed-integer programming problems have been proposed; - A majorant Lagrange-type function has been constructed for a Boolean programming problem with integer interval data, some properties of this function have been discovered, and algorithms for its minimization have been developed. As a result, the errors from the optimal solutions of the approximate solutions of these problems are estimated.