Liusheng Hou

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The augmented Lagrangian method (ALM) is a benchmark for solving a convex minimization model with linear constraints. We consider the special case where the objective is the sum of m functions without coupled variables. For solving this separable convex minimization model, it is usually required to decompose the ALM subproblem at each iteration into m(More)
We consider a multiple-block separable convex programming problem, where the objective function is the sum of m individual convex functions without overlapping variables, and the constraints are linear, aside from side constraints. Based on the combination of the classical Gauss–Seidel and the Jacobian decompositions of the augmented Lagrangian function, we(More)
It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this paper a modified trust-region method with Beale’s Preconditioned Conjugate Gradient (BPCG) technique is developed for solving unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful(More)
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