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Books > Science & Mathematics > Mathematics > Optimization
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Lagrange-type Functions in Constrained Non-Convex Optimization (Hardcover, 2003 ed.)
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Lagrange-type Functions in Constrained Non-Convex Optimization (Hardcover, 2003 ed.)
Series: Applied Optimization, 85
Expected to ship within 10 - 15 working days
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Lagrange and penalty function methods provide a powerful approach,
both as a theoretical tool and a computational vehicle, for the
study of constrained optimization problems. However, for a
nonconvex constrained optimization problem, the classical Lagrange
primal-dual method may fail to find a mini mum as a zero duality
gap is not always guaranteed. A large penalty parameter is, in
general, required for classical quadratic penalty functions in
order that minima of penalty problems are a good approximation to
those of the original constrained optimization problems. It is
well-known that penaity functions with too large parameters cause
an obstacle for numerical implementation. Thus the question arises
how to generalize classical Lagrange and penalty functions, in
order to obtain an appropriate scheme for reducing constrained
optimiza tion problems to unconstrained ones that will be suitable
for sufficiently broad classes of optimization problems from both
the theoretical and computational viewpoints. Some approaches for
such a scheme are studied in this book. One of them is as follows:
an unconstrained problem is constructed, where the objective
function is a convolution of the objective and constraint functions
of the original problem. While a linear convolution leads to a
classical Lagrange function, different kinds of nonlinear
convolutions lead to interesting generalizations. We shall call
functions that appear as a convolution of the objective function
and the constraint functions, Lagrange-type functions."
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