1 research outputs found
Univariate global optimization with multiextremal non-differentiable constraints without penalty functions
This paper proposes a new algorithm for solving constrained global
optimization problems where both the objective function and constraints are
one-dimensional non-differentiable multiextremal Lipschitz functions.
Multiextremal constraints can lead to complex feasible regions being
collections of isolated points and intervals having positive lengths. The case
is considered where the order the constraints are evaluated is fixed by the
nature of the problem and a constraint is defined only over the set where
the constraint is satisfied. The objective function is defined only over
the set where all the constraints are satisfied. In contrast to traditional
approaches, the new algorithm does not use any additional parameter or
variable. All the constraints are not evaluated during every iteration of the
algorithm providing a significant acceleration of the search. The new algorithm
either finds lower and upper bounds for the global optimum or establishes that
the problem is infeasible. Convergence properties and numerical experiments
showing a nice performance of the new method in comparison with the penalty
approach are given.Comment: 19 pages, 5 figures, 3 table