Mathematical Programming: Series A and B
New variants of bundle methods
Mathematical Programming: Series A and B
A Proximal Bundle Method Based on Approximate Subgradients
Computational Optimization and Applications
SIAM Journal on Optimization
A Proximal Bundle Method with Approximate Subgradient Linearizations
SIAM Journal on Optimization
A Method of Centers with Approximate Subgradient Linearizations for Nonsmooth Convex Optimization
SIAM Journal on Optimization
A bundle-filter method for nonsmooth convex constrained optimization
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Mixed $H_2/H_\infty$ Control via Nonsmooth Optimization
SIAM Journal on Control and Optimization
An inexact bundle variant suited to column generation
Mathematical Programming: Series A and B
Computation of Multivariate Normal and t Probabilities
Computation of Multivariate Normal and t Probabilities
An Inexact Bundle Approach to Cutting-Stock Problems
INFORMS Journal on Computing
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We propose restricted memory level bundle methods for minimizing constrained convex nonsmooth optimization problems whose objective and constraint functions are known through oracles (black-boxes) that might provide inexact information. Our approach is general and covers many instances of inexact oracles, such as upper, lower and on-demand accuracy oracles. We show that the proposed level bundle methods are convergent as long as the memory is restricted to at least four well chosen linearizations: two linearizations for the objective function, and two linearizations for the constraints. The proposed methods are particularly suitable for both joint chance-constrained problems and two-stage stochastic programs with risk measure constraints. The approach is assessed on realistic joint constrained energy problems, arising when dealing with robust cascaded-reservoir management.