Book Chapter10.1007/978-94-009-0369-2_17
Deterministic Global Optimization
Yu. G. Evtushenko,M. A. Potapov +1 more
- 01 Jan 1994
- pp 481-500
8
TL;DR: Numerical methods for finding global solutions of nonlinear programming and multi-criterial optimization problems are proposed and the sequential deterministic approach is used which is based on the non-uniform space covering technique as a general framework.
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Abstract: Numerical methods for finding global solutions of nonlinear programming and multi-criterial optimization problems are proposed. The sequential deterministic approach is used which is based on the non-uniform space covering technique as a general framework. The definitions of the e-solution for the nonlinear programming problem and the multicriterial optimization problems are given. It is shown that if all the functions, which define these problems, satisfy a Lipschitz condition and the feasible set is compact, then e-solutions can be found in the process of only one covering of the feasible set on a nonuniform net with a finite number of function evaluations. Space covering techniques are applied to solving systems of nonlinear equations and minimax problems.
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Citations
Advances in Interval Methods for Deterministic Global Optimization in Chemical Engineering
Y. Lin,Mark A. Stadtherr +1 more
TL;DR: This paper considers strategies for bounding the solution set of the linear interval equation system that must be solved in the context of the interval-Newton method, and a new bounding approach based on the use of linear programming (LP) techniques is presented.
Global Interval Methods for Local Nonsmooth Optimization
TL;DR: An interval method for determining local solutions of nonsmooth unconstrained optimization problems is discussed and prototype algorithms for both parts of the method are presented as well as a complete convergence theory for them and how outer approximations can be obtained are demonstrated.
6
Using necessary optimality conditions for acceleration of the nonuniform covering optimization method
Yury Evtushenko,Mikhail Posypkin +1 more
TL;DR: This work proposes to use necessary optimality conditions of first and second order for reducing the search for boxconstrained problems by using the non-uniform covering method and provides the algorithm description and proves its correctness.
1
Estimação de modelos de Markov ocultos usando aritmética intervalar
Tiago de Morais Montanher
- 24 Apr 2015
TL;DR: In this article, the authors study the problem of estimating the parâmetros of Markov Ocultos (MMOs) in a model of hidden Markov processes.
References
•Book
Algorithms for Minimization Without Derivatives
Richard P. Brent
- 01 Jan 1972
TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.
•Book
Numerical Optimization Techniques
Yurij G. Evtushenko
- 31 Dec 1985
TL;DR: The book of Professor Evtushenko describes both the theoretical foundations and the range of applications of many important methods for solving nonlinear programs, particularly emphasized is their use for the solution of optimal control problems for ordinary differential equations.
184
On descent from local minima
A. A. Goldstein,J. F. Price +1 more
TL;DR: In this paper, a process with analytical criteria is described which sometimes finds smaller local minima in an algorithmic manner, under the assumption that a local minimum is known, and the process to be described sometimes finds the smaller local minimizers in an analytical manner.
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