Related papers: An Alternating Trust Region Algorithm for Distribu…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of $f + h$ in a trust region. The…
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…
In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…
Modern machine learning, especially the training of deep neural networks, depends on solving large-scale, highly nonconvex optimization problems, whose objective function exhibit a rough landscape. Motivated by the success of parallel…
A stochastic second-order trust region method is proposed, which can be viewed as a second-order extension of the trust-region-ish (TRish) algorithm proposed by Curtis et al. (INFORMS J. Optim. 1(3) 200-220, 2019). In each iteration, a…
Transmission network expansion planning is a mixed-integer optimization problem, whose solution is used to guide future investment in transmission equipment. An approach is presented to find the global solution of the transmission planning…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
Adaptive trust-region methods attempt to maintain strong convergence guarantees without depending on conservative estimates of problem properties such as Lipschitz constants. However, on close inspection, one can show existing adaptive…
We prove global convergence of a bundle trust region algorithm for non-smooth non-convex optimization, where cutting planes are generated by oracles respecting four basic rules. The benefit is that convergence theory applies to a large…
We consider descent methods for solving non-finite valued nonsmooth convex-composite optimization problems that employ Gauss-Newton subproblems to determine the iteration update. Specifically, we establish the global convergence properties…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
Nowadays stochastic approximation methods are one of the major research direction to deal with the large-scale machine learning problems. From stochastic first order methods, now the focus is shifting to stochastic second order methods due…
This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to…
In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…