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An asynchronous proximal bundle method
We develop a fully asynchronous proximal bundle method for solving non-smooth, convex optimization problems. The algorithm can be used as a drop-in...
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A bundle-type method for nonsmooth DC programs
A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact...
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A preconditioned iterative interior point approach to the conic bundle subproblem
The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite...
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Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm
This paper develops an iterative algorithm to solve nonsmooth nonconvex optimization problems on complete Riemannian manifolds. The algorithm is...
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A single cut proximal bundle method for stochastic convex composite optimization
This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex function, and...
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Implementation of an oracle-structured bundle method for distributed optimization
We consider the problem of minimizing a function that is a sum of convex agent functions plus a convex common public function that couples them. The...
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A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems
We propose a class of infeasible proximal bundle methods for solving nonsmooth nonconvex multi-objective optimization problems. The proposed...
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Finite Difference Method on Flat Surfaces with a Flat Unitary Vector Bundle
We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a tileable surface with a flat...
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A new restricted memory level bundle method for constrained convex nonsmooth optimization
In this paper, a new restricted memory level bundle method for solving constrained convex nonsmooth optimization problems is proposed. To ensure...
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Direct minimizing method for Yang–Mills energy over SO(3) bundle
In this paper, we improve the known results on the direct minimizing method for Yang–Mills energy over closed four manifolds when the structure group...
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Linear Convergence of the Derivative-Free Proximal Bundle Method on Convex Nonsmooth Functions, with Application to the Derivative-Free \(\mathcal{VU}\)-Algorithm
Proximal bundle methods are a class of optimisation algorithms that leverage the proximal operator to address nonsmoothness in the objective function...
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Convergence of the proximal bundle algorithm for nonsmooth nonconvex optimization problems
A proximal bundle algorithm is proposed for solving unconstrained nonsmooth nonconvex optimization problems. At each iteration, using already...
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Density of rational points on some quadric bundle threefolds
We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of...
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An Inexact Bundle Method and Subgradient Computations for Optimal Control of Deterministic and Stochastic Obstacle Problems
The aim of this work is to develop an inexact bundle method for nonsmooth nonconvex minimization in Hilbert spaces and to investigate its application...
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A bundle method for nonsmooth DC programming with application to chance-constrained problems
This work considers nonsmooth and nonconvex optimization problems whose objective and constraint functions are defined by difference-of-convex (DC)...
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A filter proximal bundle method for nonsmooth nonconvex constrained optimization
A filter proximal bundle algorithm is presented for nonsmooth nonconvex constrained optimization problems. The new algorithm is based on the proximal...
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Acceleration techniques for level bundle methods in weakly smooth convex constrained optimization
We develop a unified level-bundle method, called accelerated constrained level-bundle (ACLB) algorithm, for solving constrained convex optimization...
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Polyak Minorant Method for Convex Optimization
In 1963 Boris Polyak suggested a particular step size for gradient descent methods, now known as the Polyak step size, that he later adapted to...
