Critical point approximation through exact regularization

Authors:
Enrique Fernández Cara and Carlos Moreno

Journal:
Math. Comp. **50** (1988), 139-153

MSC:
Primary 65K10; Secondary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917822-3

MathSciNet review:
917822

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Abstract: We present several iterative methods for finding the critical points and/or the minima of a functional which is essentially the difference between two convex functions. The underlying idea relies upon partial and exact regularization of the functional, which allows us to preserve the local feature in a large number of applications, as well as to obtain some convergence results. These methods are further applied to some differential problems of the semilinear elliptic type arising in plasma physics and fluid mechanics.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917822-3

Keywords:
Nonconvex optimization,
exact regularization,
semilinear elliptic problems with discontinuous nonlinearities,
plasma confinement,
vortex rings

Article copyright:
© Copyright 1988
American Mathematical Society