Hessian Riemannian gradient flows in convex programming
In view of solving theoretically constrained minimization problems, we investigate the
properties of the gradient flows with respect to Hessian Riemannian metrics induced by …
properties of the gradient flows with respect to Hessian Riemannian metrics induced by …
On the convergence of gradient-like flows with noisy gradient input
P Mertikopoulos, M Staudigl - SIAM Journal on Optimization, 2018 - SIAM
In view of solving convex optimization problems with noisy gradient input, we analyze the
asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we …
asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we …
A continuous dynamical Newton-like approach to solving monotone inclusions
H Attouch, BF Svaiter - SIAM Journal on Control and Optimization, 2011 - SIAM
We introduce nonautonomous continuous dynamical systems which are linked to the
Newton and Levenberg–Marquardt methods. They aim at solving inclusions governed by …
Newton and Levenberg–Marquardt methods. They aim at solving inclusions governed by …
Fenchel conjugate via Busemann function on Hadamard manifolds
GC Bento, JC Neto, ÍDL Melo - Applied Mathematics & Optimization, 2023 - Springer
In this paper we introduce a Fenchel-type conjugate, given as the supremum of convex
functions, via Busemann functions. It is known that Busemann functions are smooth convex …
functions, via Busemann functions. It is known that Busemann functions are smooth convex …
An inexact proximal point algorithm for maximal monotone vector fields on Hadamard manifolds
G Tang, N Huang - Operations Research Letters, 2013 - Elsevier
In this paper, an inexact proximal point algorithm concerned with the singularity of maximal
monotone vector fields is introduced and studied on Hadamard manifolds, in which a …
monotone vector fields is introduced and studied on Hadamard manifolds, in which a …
Barrier operators and associated gradient-like dynamical systems for constrained minimization problems
J Bolte, M Teboulle - SIAM journal on control and optimization, 2003 - SIAM
We study some continuous dynamical systems associated with constrained optimization
problems. For that purpose, we introduce the concept of elliptic barrier operators and …
problems. For that purpose, we introduce the concept of elliptic barrier operators and …
[图书][B] SOC functions
JS Chen, JS Chen - 2019 - Springer
During the past two decades, there have been active research for second-order cone
programs (SOCPs) and second-order cone complementarity problems (SOCCPs). Various …
programs (SOCPs) and second-order cone complementarity problems (SOCCPs). Various …
Local search proximal algorithms as decision dynamics with costs to move
H Attouch, A Soubeyran - Set-Valued and Variational Analysis, 2011 - Springer
Acceptable moves for the “worthwhile-to-move” incremental principle are such that
“advantages-to-move” are higher than some fraction of “costs-to-move”. When combined …
“advantages-to-move” are higher than some fraction of “costs-to-move”. When combined …
Analyzing the impact of regularization on REMSE
The spectral density of a multidimensional stationary process or a homogeneous random
field can be inferred through the REgularized Multidimensional Spectral Estimator (REMSE) …
field can be inferred through the REgularized Multidimensional Spectral Estimator (REMSE) …
Singular Riemannian barrier methods and gradient-projection dynamical systems for constrained optimization
This work is devoted to the dynamical system (SRB): d (∂ h (x (t)))/dt+∇ Φ (x (t))∋ 0, with ha
proper lower semicontinuous convex function. Existence and uniqueness of solutions are …
proper lower semicontinuous convex function. Existence and uniqueness of solutions are …