Deterministic and stochastic methods for solving extremal problems
|
StatusThe thesis was presented on the 12 May, 2010Approved by NCAA on the 5 July, 2010 Abstract – 0.31 Mb / in romanian |
Keywords
convex optimization, differentiable and nondifferentiable functions, gradient, subgradient, deterministic and stochastic methods, minimax problem, almost certain convergence (with probability 1)Summary
The thesis contains the introduction, three chapters, conclusions and recommendations, the bibliography (108 titles) , 2 annexes and consists of 153 pages, from which 97 pages of the main part, including 6 figures and 14 tables. Obtained results are published in 11 scientific papers.
The area of study refers to the research and solution of a set of problems from mathematical optimization. These problems are described by convex nonlinear models. Minimax problem has an important place among them.
The aim of this work consists in following: development of deterministic and stochastic methods for solving nonlinear optimization models of general form; description of fundamental differences between elaborated methods and existing ones; to expose the range of the problems that fit best for solving using described methods in comparison with existing methods; description of theoretical aspects of proposed methods; development of software.
The scientific novelty and originality of obtained results consist in: presentation of new methods for solving a problem characterized by a differentiable convex model (all these methods are generalizing gradient method); description of two methods based on the subgradient for solving a minimax nondifferentiable problem with restrictions; proposed methods are of deterministic or stochastic nature.
The theoretical signification consists in: proposed methods solve problems of convex programming of general form, inclusively a minimax problem. Such problems are often encountered in applied domains. Described methods contain rigorous theoretical argumentation. Convergence conditions have been formulated with detailed demonstrations for all of them.
The practical value of the work: for every proposed method has been developed a program. Elaborated software is simple, efficient and does not require considerable computing resources.
Oficial Reviewers
- Dumitru Solomon
doctor habilitat, associate professor (docent), Moldova State University - Vasile Moraru
doctor, professor, Technical University of Moldova
Council's Members
- Petru Soltan, president
doctor habilitat, professor, Moldova State University - Sergiu Cataranciuc, secretary
doctor habilitat, professor, Moldova State University - Dumitru Lozovanu, member
doctor habilitat, professor, Moldova State University - Gheorghe Mişcoi, member
doctor habilitat, professor, Institute of Mathematics and Computer Science - Boris Hâncu, member
doctor, associate professor (docent), Moldova State University
Theses
