A Shifted-Barrier Primal-Dual Algorithm Model for Linearly ConstrainedOptimization Problems
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Nonmonotonic back-tracking trust region interior point algorithm for linear constrained optimization
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Convergence Properties of Dikin"s Affine Scaling Algorithm for Nonconvex Quadratic Minimization
Journal of Global Optimization
Newton-KKT interior-point methods for indefinite quadratic programming
Computational Optimization and Applications
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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.