On the exactness of a class of nondifferentiable penalty functions
Journal of Optimization Theory and Applications
Exact penalty functions in constrained optimization
SIAM Journal on Control and Optimization
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
A comparison of complete global optimization solvers
Mathematical Programming: Series A and B
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
On the Convergence of Augmented Lagrangian Methods for Constrained Global Optimization
SIAM Journal on Optimization
Unified theory of augmented Lagrangian methods for constrained global optimization
Journal of Global Optimization
Computational Optimization and Applications
A partition-based global optimization algorithm
Journal of Global Optimization
Global minimization using an Augmented Lagrangian method with variable lower-level constraints
Mathematical Programming: Series A and B
An artificial fish swarm algorithm based hyperbolic augmented Lagrangian method
Journal of Computational and Applied Mathematics
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In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty approach. In particular, we make use of a non-differentiable exact penalty function $${P_q(x;\varepsilon)}$$ . We show that, under weak assumptions, there exists a threshold value $${\bar \varepsilon 0 }$$ of the penalty parameter $${\varepsilon}$$ such that, for any $${\varepsilon \in (0, \bar \varepsilon]}$$ , any global minimizer of P q is a global solution of the related constrained problem and conversely. On these bases, we describe an algorithm that, by combining an unconstrained global minimization technique for minimizing P q for given values of the penalty parameter $${\varepsilon}$$ and an automatic updating of $${\varepsilon}$$ that occurs only a finite number of times, produces a sequence {x k } such that any limit point of the sequence is a global solution of the related constrained problem. In the algorithm any efficient unconstrained global minimization technique can be used. In particular, we adopt an improved version of the DIRECT algorithm. Some numerical experimentation confirms the effectiveness of the approach.