STUDIJ?  PROGRAMA


OPTIMIZAVIMO METODAI IR TAIKYMAI

Prof., hab.dr. J.Mockus 


Santrauka

Nagrinejami pagrindiniai optimizavimo u?daviniai bei ju?sprendimo
metodai:
-  Tiesinis,  stochastinis bei dinaminis
programavimas.
-  Lokalaus ir globalaus optimizavimo
metodai.  
- Diskretus optimizavimas 
- Pareto optimalumas (vektorinis optimizavimas).

Nurodomi labiausia paplit algoritmai.  Aptariama optimizavimo
programin? ?ranga.    Nagrinejant visas kurso dalis nu?vieciama praktinio
optimizavimo metod? taikymo specifika ir patyrimas.  Skaitant teorin? kursa  demonstruojamas
 atitinkamos programines ?rangos darbas. Teorija pateikiama  sinchronizuotai su laboratoriniais darbais atliekamais naudojant programine irang?.
skirt? ?ioms studijoms.

Didelis d?mesys skiriamas optimizavimo taikymo galimybi? teoriniam pagrindimui bei praktini? ?gud?i? ?sigyjimui. 
?iuo tikslu parinkta eil? charaktering? u?davini? atspindinci? svarb taikymo sritis.
Parinkti u?davinai nagrinejami kaip optimizavimo metod? taikymo pavyzd?iai. 
U?daviniai parinkti taip, kad jie gal?tu iliustruoti 
optimizavimo klausimus charakteringus pla?ioms praktini? u?davini? ?eimoms. 

Tikslu  u?tikrinti glaud? rys? tarp disciplin?,  numatoma studijuoti optimizaciniustuos  operaciju tyrimo bei losimu ir rinkos teorijos modelius.

Konkre?iai optimizavimo metodai bus nagrin?jami:
- pusiausvyros situacijai rasti konkurencin?je aplinkoje,
tai Nash'o ir Walras'o modeliai, 
ekonomin? dvikova, optimali inspektavimo strategija,
- prognoz?s modeli? parametrams ?vertinti,
tai ARMA bei kintam? masteli? modeliai,
- optimaliems tvarkara?c?iams sudaryti,
tai mokykl? bei "siuvykl?" modeliai
- nuosekli? sprendim? pri?mimui,
tai optimalus pirkimo momentas 

Kiekvienas studentas isprend?ia bent vien? savo pasirinkt? u?davin? naudodamas priemones ir pavyzd?ius pateiktus nuotolini? studij?  tinklapyje
http://soften.ktu.lt/~mockus

LITERATURA

A. ?ilinskas,
"Matematinis Programavimas",
Kaunas, VDU, 2000 

A.?ilinskas, V.?altenis,
"Poisk optimuma", 
Hauka, Moskva, 1989

V.?altenis, A.?ilinskas, 
"Technini? optimizavimo u?davini? sprendimas", 
Vilnius, Mokslas, 1986

A. ?ilinskas
"Naujieji projektavimo metodai"
Vilnius, Mokslas, 1990

F. Peldschus, E.K. Zavadskas
"Matriciniai lo?imai technologijoje ir vadyboje"
Vilnius, Technika, 1997

J.B.Mockus, 
"Mnogoekstremalnye zadaci v proektirovanii", 
Nauka, Moskva, 1967.

J. Mockus, 
"Bayesian Approach to Global Optimization", 
Kluwer Academic Publishers, Dordrecht-Boston-London, 1989

J. Mockus et al.,
"Bayesian Heuristic Approach to Discrete and Global Optimization"
Kluwer Academic Publishers, Boston, 1997,
eletronic version  'book.pdf' in  the websites including  'http://soften.ktu.lt/~mockus'

J. Mockus, "A Set of Examples of Global and Discrete Optimization: Application of Bayesian Heuristic Approach",
Kluwer Academic Publishers, Dordrecht-Boston-London, 2000 ,
electronic vetsions 'stud2.pdf' and 'stud?nn.html' in t
http://soften.ktu.lt/~mockus

J. Mockus,
"A set of examples of global and discrete optimization: application of Bayesian heuristic approach I",
Informatica, 
vol 8,
p 237-264,
num 2, 1997

J. Mockus,
"A set of examples of global and discrete optimization: application of Bayesian heuristic approach II",
Informatica, 
vol 8,
p 495-526,
num 4, 1997

E.S. Ventcel, 
"Issledovanioe operacii"
Sovetskoe Radio, Moskva, 1972.

D. Himmelblau, 
"Prikladnoe nelineinoe programmirovanie", 
Mir, Moskva, 1975


A.?ilinskas, 
"Globalnaja optimizacija", 
Mokslas, Vilnius, 1986

M. De Groot, 
"Optimalnye statisticeskie resenija", 
Mir, Moskva, 1974.

Ju. M. Ermoljev, 
"Metody stochasticeskovo programmirovanija", 
Hauka, Moskva, 1976.

James O. Berger, 
"Statistical Decision Theory and Bayesian Analysis",
Springer-Verlag, New York, 1985

Yu. Ermoljev, R. Wets, 
"Numerical Techniques for StochasticOptimization", 
Springer-Verlag, Berlin,1980.

E.G.Davydov, 
"Issledovanie Operacii", 
Vyssaja skola, Moskva, 1990.

EGZAMINAI:  1 (po 15 savai?i?)

KONTROLINIAI DARBAI: 1 (po 8 savai?i?)


Resume

The following important optimization problems and methods of 
solution are regarded.
- linear, discrete, stochastic, and dynamic programming,
- local and global methods of non-linear optimization,
- discrete optimization,
- Pareto optimality (multi-objective optimization)

The most popular and efficient algorithms are discussed.
The optimization software is described.
The theoretical aspects are regarded in connection with real-life aplications
 considering a set of specific mathematical models.
- search for equilibrium in competitive environment,
- Portfolio problem (optimal investment)
- Duel model (optimal startegy of differential game)
- Bride's problem (optimal sequential decisions)
- Scheduling model (Bayesian heuristic approach)

Each student solves by computer at least one example of his\her choice using the software system  available in the web-site
http://soften.ktu.lt/~mockus