A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization
RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS
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This work presents a global convergence theory for a broad class of trust-region algorithms for the smooth nonlinear programming problem with equality constraints. The main result generalizes Powells 1975 result for unconstrained trust-region algorithmic. The trial step is characterized by very mild conditions on its normal tangential components. The normal Component need not be computed accurately. The theory requires a quasi-normal component to satisfy a fraction of Cauchy decrease condition on the quadratic model of the linearized constraints. The tangential component then must satisfy a fraction of Cauchy decrease condition of a quadratic model of the Lagrasigian function in the translated tangent space of the constraints determined by the quasi-normal component.
- Numerical Mathematics
- Operations Research