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ConicBundle
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Classes | |
| class | ConicBundle::Groundset |
| abstract representation of the feasible convex ground set to be optimized over, provides the QP solver for the bundle subproblem as well as routines for computing feasible points and ground set aggregates More... | |
| class | ConicBundle::UnconstrainedGroundset |
| implements an unconstrained groundset More... | |
| class | ConicBundle::LPGroundset |
| represents a polyhedral feasible ground set by affine constraints as in Linear Programming with special support for simple box constraints More... | |
In nonsmooth convex optimization, ground sets are typically very simple, mostly the entire space or some box. While there is special support for these simple groundsets, the package currently also offers general LP-constrained groundsets, but in this case computations can be expected to be more involved.
In ConicBundle box constrained ground sets may be treated directly by a QPSolver handling constraint or by an (unconstrained) UQPSolver in a Gauss-Seidel manner within the process of solving the bundle subproblem for determining the next candidate. To describe the essence of the second approach, convergence builds upon maintaining two aggregate subgradients, one for the cost function and one for the ground set. The basic assumption is that the indicator function of the ground set is understood sufficiently well so that a special aggregate subgradient of this indicator function can be generated directly (by some polynomial algorithm) with the following property. Given a feasible center y and any fixed aggregate of the cost function, the groundset aggregate gives rise to the proximal point over the cutting model generated by all subgradients of the characteristic function plus the fixed cost function aggregate. In particular, this proximal point is always feasible. The class Groundset has to provide the functionality to compute a feasible starting point and to compute this ground set aggregate.
1.8.13