Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Nghia, Tran T. A."'
In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are $\mathcal{C}^2$-cone reducible. Our approach, by using Robinson's strong
Externí odkaz:
http://arxiv.org/abs/2409.13118
Autor:
Nghia, Tran T. A.
In this paper, we mainly study tilt stability and Lipschitz stability of convex optimization problems. Our characterizations are geometric and fully computable in many important cases. As a result, we apply our theory to the group Lasso problem and t
Externí odkaz:
http://arxiv.org/abs/2402.05215
In this paper, we mainly study solution uniqueness of some convex optimization problems. Our characterizations of solution uniqueness are in terms of the radial cone. This approach allows us to know when a unique solution is a strong solution or even
Externí odkaz:
http://arxiv.org/abs/2401.10346
In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative conditions for this
Externí odkaz:
http://arxiv.org/abs/2308.09224
In this paper, we show the important roles of sharp minima and strong minima for robust recovery. We also obtain several characterizations of sharp minima for convex regularized optimization problems. Our characterizations are quantitative and verifi
Externí odkaz:
http://arxiv.org/abs/2111.05444
This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We prove that the
Externí odkaz:
http://arxiv.org/abs/1903.05746
Autor:
Fadili, Jalal1 (AUTHOR), Nghia, Tran T A2 (AUTHOR) nttran@oakland.edu, Tran, Trinh T T2 (AUTHOR)
Publikováno v:
Information & Inference: A Journal of the IMA. Sep2023, Vol. 12 Issue 3, p1461-1513. 53p.
The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradient
Externí odkaz:
http://arxiv.org/abs/1708.06631
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of unconstra
Externí odkaz:
http://arxiv.org/abs/1705.09745
We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of semi-simpleness of all e
Externí odkaz:
http://arxiv.org/abs/1407.0671