Unconstrained Global Optimization Problems Research Articles

Unconstrained global optimization using stochastic intergral equations

A stochastic method is described for solving unconstrained global optimization problems based on a special class of stochastic integral equations. An efficient algorithm is developed using a semi-implicit Euler method for the numerical solution of the stochastic integral equations. Interesting properties and a parallel implementation of the algorithm enable the treatment of problems with a large number of variables

Global optimization for satisfiability (SAT) problem

The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. Following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, which transforms the discrete SAT problem on Boolean space {0, 1}/sup m/ into an unconstrained global optimization problem on real space E/sup m/. A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtracking/resolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF) formulas. It offers a complementary approach to the existing SAT algorithms. >

Nonlinear coordinate transformations for unconstrained optimization I. Basic transformations

In this two-part article, nonlinear coordinate transformations are discussed to simplify unconstrained global optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems are quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of variables to be optimized can be reduced. Otherwise the analysis of the structure can serve as a first phase for solving unconstrained global optimization problems.

Computational algorithms based on random search for solving global optimization problems

Computational algorithms based on random search approach for solving unconstrained and con-strained global optimization problems have been proposed and tested on a number of test problems taken from literature. The results show that the proposed algorithms can be used to solve moderately sized unconstrained, inequality constrained and a class of equality constrained global optimization problems.