Iterative methods for large convex quadratic programs: a survey
SIAM Journal on Control and Optimization
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Dual coordinate ascent methods for non-strictly convex minimization
Mathematical Programming: Series A and B
Parallel Gradient Distribution in Unconstrained Optimization
SIAM Journal on Control and Optimization
New Inexact Parallel Variable Distribution Algorithms
Computational Optimization and Applications
Error bounds in mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Two-phase model algorithm with global convergence for nonlinear programming
Journal of Optimization Theory and Applications
Testing Parallel Variable Transformation
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Computational Optimization and Applications
On the Convergence of Constrained Parallel Variable Distribution Algorithms
SIAM Journal on Optimization
Parallel Variable Transformation in Unconstrained Optimization
SIAM Journal on Optimization
A Truncated SQP Method Based on Inexact Interior-Point Solutions of Subproblems
SIAM Journal on Optimization
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In the parallel variable distribution framework for solving optimization problems (PVD), the variables are distributed among parallel processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining “secondary” variables to change in a restricted fashion along some easily computable directions. For constrained nonlinear programs convergence theory for PVD algorithms was previously available only for the case of convex feasible set. Additionally, one either had to assume that constraints are block-separable, or to use exact projected gradient directions for the change of secondary variables. In this paper, we propose two new variants of PVD for the constrained case. Without assuming convexity of constraints, but assuming block-separable structure, we show that PVD subproblems can be solved inexactly by solving their quadratic programming approximations. This extends PVD to nonconvex (separable) feasible sets, and provides a constructive practical way of solving the parallel subproblems. For inseparable constraints, but assuming convexity, we develop a PVD method based on suitable approximate projected gradient directions. The approximation criterion is based on a certain error bound result, and it is readily implementable. Using such approximate directions may be especially useful when the projection operation is computationally expensive.