The main objective is to develop, to test and to apply a
graduate studies and research cooperation in the Internet environment.
The system involves the theory, a set of examples and the software for the Internet environment.
The scientific topic is modeling and optimization of economic, social and engineering systems.
Theoretical background is the Theory of Games and Markets .
The optimization methods implement the Bayesian Heuristic Approach to Global and Discrete Optimization that is based on the Statistical Decision Theory.
1. New Theoretical Results:
The Bayesian Approach is well known and used in the theory of statistical decisions and statistics.
Heuristic methods is an important part in knowledge based systems and artificial intelligence. They are widely used while solving real-life problems of global and discrete optimization.
The new Bayesian Heuristic methods "BHA" optimize parameters of the well-known heuristics and help to develop new heuristics.
1. New Applications:
The Bayesian Heuristic Approach is used searching for equilibrium in a number of models of games and markets. These include:
Two types of competitive models;
models of "static" competition "WALRAS" and
a model of dynamic competition "ECODUEL" ,
Optimal investment models, including
the portfolio model "PORTFOLIO" .
An stock-exchange model is " STOCK-GAME"' Parameter optimization of an Auto-Regressive model minimizing absolute deviations is in " AR-ABS" .
Important application area of the Bayesian Heuristic Approach is the optimal scheduling.
An example is the profiled school scheduling "SCHOOL" click "Vidunas".
The bimatrix games problem is illustrated by the example of "Irrelevant Fraud" (IF) method "RANGER" .
Huge practical potential of Statistical Decisions Theory shows a set of "Brides" problems "BRIDE" . These include various applications. For example:
"FLAT" click "Buy-a-Flat".
An optimal diet problem is to illustrate applications of multi-objective optimization and linear programming " DIET" .
Application in Studies
1. Application in graduate studies: The objective is to narrow the gap between the theory and applications. The lecture notes are in Lithuanin as a set of slides " SLIDES" The framework for global optimization methods and 'on-line' models "GMJ"
2. Application in direct distance studies:
The objective is to
make the lectures available "on-line" for students of various
and foreign universities.
The lectures are broadcasting by video-conferencing at fixed times:
on Friday, 8:00-9:30 AM.
An example is the opening lecture "INTRO" . All the students taking part in the video-conferencing can see and hear the same stuff. They can ask questions, too, and all connected see and hear these questions and professor's answers.
3.Application to individual studies: The objective is to present equal opportunities for those that cannot attend the class-rooms. That is achieved by personal Internet connection to the central video-conferencing class "VIDEO" .
4. Application to home work: The objective
is to present a choice
to make the home work interesting .
There are some suggestions "HOME" however, the final decisions are made by students
The outline of general theoretical results is in a set of slides "SLIDES" . The slides are accompanied by book-marks explaining the content.
A Set of Examples
The basic set of examples, including theoretical background
description, is given as a book in 'pdf' file
However, the main set of examples is dynamic and is presented in web-sites "EXAMPLES" .
Complete description of the Bayesian Heuristic Approach and
methods of global and discrete optimization is in two books "
BOOK" and "MODELS"
The general references are:
- Optimization Methods "OM"
- Theory of Games and Markets "OR"
- Mathematical Programming (textbook in Lithuanian):
Matematinis Programavimas (pdf)
Web-Sitesthe international mirror: http://mockus.org/optimum