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We consider the global optimization of a nonsmooth (nondifferentiable) nonconvex real function. We introduce a variable metric descent method adapted to nonsmooth situations, which is modified by the incorporation of suitable random perturbations. Convergence to a global minimum is established and a simple method for the generation of suitable perturbations is introduced. An algorithm is proposed and numerical results are presented, showing that the method is computationally effective and stable....
A reformulation of a mathematical program is a formulation which
shares some properties with, but is in some sense better than, the
original program. Reformulations are important with respect to the
choice and efficiency of the solution algorithms; furthermore, it is
desirable that reformulations can be carried out
automatically. Reformulation techniques are widespread in mathematical
programming but interestingly they have never been studied under a
unified framework. This paper attempts to move...
In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions.
In this paper, we consider a class of stochastic
mathematical programs with equilibrium constraints (SMPECs) that
has been discussed by Lin and Fukushima (2003). Based on a
reformulation given therein, we propose a regularization method
for solving the problems. We show that, under a weak condition, an
accumulation point of the generated sequence is a feasible point
of the original problem. We also show that such an accumulation
point is S-stationary to the problem under additional assumptions....
In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an -optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) -convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) -optimal solutions of the multi-dimensional...
New positive definite preconditioners for the matrix free truncated Newton method are given. Corresponding algorithms are described in detail. Results of numerical experiments that confirm the efficiency and robustness of the preconditioned truncated Newton method are reported.
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