Analysis of a Cutting Plane Method That Uses Weighted Analytic Center and Multiple Cuts
We consider the analytic center cutting plane (or column generation) algorithm for solving general convex problems defined by a separation oracle. The oracle is called at an approximate analytic cent...
We consider the analytic center cutting plane (or column generation) algorithm for solving general convex problems defined by a separation oracle. The oracle is called at an approximate analytic cent...
Tensor Methods for Large, Sparse Unconstrained Optimization
Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optim., 1 (1991), pp. 293--315], who described these methods for small- to moderate-sized problems. T...
Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optim., 1 (1991), pp. 293--315], who described these methods for small- to moderate-sized problems. T...
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A Trust Region Interior Point Algorithm for Linearly Constrained Optimization
SIAM J. Optim. Volume 7, Issue 3, pp. 717-731 (1997)
Issue Date: 1997
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We present an extension, for nonlinear optimization under linear constraints, of an algorithm for quadratic programming using a trust region idea introduced by Ye and Tse [Math. Programming, 44 (1989), pp. 157--179] and extended by Bonnans and Bouhtou [RAIRO Rech. Opér., 29 (1995), pp. 195--217]. Due to the nonlinearity of the cost, we use a linesearch in order to reduce the step if necessary. We prove that, under suitable hypotheses, the algorithm converges to a point satisfying the first-order optimality system, and we analyze under which conditions the unit stepsize will be asymptotically accepted.
©1997 Society for Industrial and Applied Mathematics| Permalink: | http://dx.doi.org/10.1137/S1052623493250639 |
KEYWORDS and AMS
90C30, 65K05, 49M40
PUBLICATION DATA
1052-6234 (print)
1095-7189 (online)
SIAM