ConicBundle is a callable library for C/C++ that implements a bundle method for solving

$min_{y\in\mathbf{R}^m}\quad f_1(y) + ... + f_k(y)$

for convex functions $f_j:\mathbf{R}^n\to\mathbf{R}$ , $j=1,...,k$ .

In addition to the standard first order oracle interface the library offers a number of special features:

Upper and lower bounds may be specified for each design variable ( $l_i\le y_i \le u_i$ ); in a less efficient and somewhat experimental variant general linear constraints are allowed, as well.
Instead of one common cutting plane model for the entire objective function, each function may either have its own specialized cutting model – this may help to improve convergence – or it may be grouped together with others in a common standard cutting plane model.
It provides substantial support for Lagrangian relaxation, i.e., if the problem corresponds to finding the optimal dual multipliers obtained by relaxing linear constraints in a relaxation or decomposition of a primal problem.
- It allows to generate approximate primal optimal solutions.
- It supports cutting plane approaches by allowing dynamic addition and deletion of dual variables without loss of quality in the cutting models.
The code offers special cutting models for linear programs over the second order cone and the cone of real symmetric positive semidefinite matrices.

The library comes with three variants of interfaces:

Interface to ConicBundle for the Language C
Interface to ConicBundle for the Language C++
Interface to ConicBundle for the Language C++ using Matrix Classes The text there gives a short introduction and the interface offers the most but may require more time to get acquainted with. It includes
- an abstract first order oracle ConicBundle::MatrixFunctionOracle for general convex functions with an example implemention of MatrixFunctionOracle (NNCBoxSupportFunction)
- a specialized box oracle with special purpose cutting model which together with a ConicBundle::AffineFunctionTransformation supports Lagrangian relaxation of linear programs over box constrained domains
- an abstract positive semidefinite cone oracle (ConicBundle exploits this in a special purpose model for the semidefinite cone or, equivalently, for maximum eigenvalue functions) and an implemention of a PSCOracle (PSCAffineFunction)
- an abstract second order cone oracle (ConicBundle exploits this in a special purpose model for the second order cone) and an implemention of a SOCOracle (SOCSupportFunction)
- all oracles can be combined with affine function transformations of the form $\delta +b^Ty+\rho f(c+Ay)$ (see ConicBundle::AffineFunctionTransformation)
- each oracle may be used either as an objective function or as a penalty function with fixed or adaptive penalty factor, see ConicBundle::MatrixCBSolver::add_function()
- dynamic submodel selection allows to optimize various oracles jointly as a sum of convex functions where each oracle's model moves between being part of a common general cutting model and forming a dedicated cutting model
- support for various Quadratic Proximal Terms with support for Variable Metric
- regarding the groundset of the design variables there is special support for (see ConicBundle::MatrixCBSolver::init_problem())
  - unconstrained ground sets (no constraints on the design variables)
  - box constrained ground sets (upper and lower bounds on each variable)
  - linearly constrained ground sets (may be significantly slower, testing was limited to simple instances so far)
- dynamic modification support for adding/deleting/modifying variables, oracles and constraints (needed e.g. for Lagrangian relaxations of cutting planes; see also the Tutorial Implementation of the SDP Max-Cut Relaxation with Triangle Separation)

The first two interfaces only use standard types and constructs of the respective languages, the third interface relies heavily on a subpackage of matrix classes also provided with this software.

Here is some more information on details (in part yet to come):

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