Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
A generalized second-order derivative in nonsmooth optimization
SIAM Journal on Control and Optimization
Quadratic approximations in convex nondifferentiable optimization
SIAM Journal on Control and Optimization
New variants of bundle methods
Mathematical Programming: Series A and B
Solving semidefinite quadratic problems within nonsmooth optimization algorithms
Computers and Operations Research
A bundle-Newton method for nonsmooth unconstrained minimization
Mathematical Programming: Series A and B
Efficiency of proximal bundle methods
Journal of Optimization Theory and Applications
Bundle-based relaxation methods for multicommodity capacitated fixed charge network design
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Quasi-Newton Bundle-Type Methods for Nondifferentiable Convex Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
On $\mathcalVU$-theory for Functions with Primal-Dual Gradient Structure
SIAM Journal on Optimization
Minimizing Nonconvex Nonsmooth Functions via Cutting Planes and Proximity Control
SIAM Journal on Optimization
New approaches for optimizing over the semimetric polytope
Mathematical Programming: Series A and B
A **-algorithm for convex minimization
Mathematical Programming: Series A and B
A Proximal Bundle Method with Approximate Subgradient Linearizations
SIAM Journal on Optimization
An Incremental Method for Solving Convex Finite Min-Max Problems
Mathematics of Operations Research
A Proximal-Projection Bundle Method for Lagrangian Relaxation, Including Semidefinite Programming
SIAM Journal on Optimization
An inexact bundle variant suited to column generation
Mathematical Programming: Series A and B
On the choice of explicit stabilizing terms in column generation
Discrete Applied Mathematics
A proximal cutting plane method using Chebychev center for nonsmooth convex optimization
Mathematical Programming: Series A and B
Piecewise linear approximations in nonconvex nonsmooth optimization
Numerische Mathematik
Gradient set splitting in nonconvex nonsmooth numerical optimization
Optimization Methods & Software - DEDICATED TO PROFESSOR VLADIMIR F. DEMYANOV ON THE OCCASION OF HIS 70TH BIRTHDAY
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We present a bundle method for convex nondifferentiable minimization where the model is a piecewise-quadratic convex approximation of the objective function. Unlike standard bundle approaches, the model only needs to support the objective function from below at a properly chosen (small) subset of points, as opposed to everywhere. We provide the convergence analysis for the algorithm, with a general form of master problem which combines features of trust region stabilization and proximal stabilization, taking care of all the important practical aspects such as proper handling of the proximity parameters and the bundle of information. Numerical results are also reported.