A Multicriteria Decision Support System MultiDecision-1

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making."

Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

Reduction Measurements for Calculation in Fuzzy Experiment Scheme

The papers is dedicated to the questions of modeling and basing super-resolution measuring- calculating systems in the context of the conception “device + PC = new possibilities”. By the authors of the article the new mathematical method of solution of the multi-criteria optimization problems was developed. The method is based on physic-mathematical formalism of reduction of fuzzy disfigured measurements. It is shown, that determinative part is played by mathematical properties of physical models of the object, which is measured, surroundings, measuring components of measuring-calculating systems and theirs cooperation as well as the developed mathematical method of processing and interpretation of measurements problem solution.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Codifferentiable Mappings with Applications to Vector Optimality

AMS subject classification: Primary 49J52; secondary: 26A27, 90C48, 47N10.

Multicriteria Evaluation and Optimization of Hierarchical Systems

It is shown that any multicriteria problem can be represented by a hierarchical system. Separate properties of the object are evaluated at the lower level of the system, using a criteria vector, and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriteria problems of evaluation and optimization. It is based on nested scalar convolutions of vector- valued criteria and allows simple structural and parametrical synthesis of multicriteria hierarchical systems.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

Exact Discriminant Function Design Using Some Optimization Techniques

Some aspects of design of the discriminant functions that in the best way separate points of predefined final sets are considered. The concept is introduced of the nested discriminant functions which allow to separate correctly points of any of the final sets. It is proposed to apply some methods of non-smooth optimization to solve arising extremal problems efficiently.

Mathematical Optimization for the Train Timetabling Problem

AMS Subj. Classification: 90C57; 90C10;

Optimization of Advertising Resources over Time: A Strategic Analysis

AMS subject classification: 90B60, 90B50, 90A80.

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.