Related papers: Decomposition Method for Lipschitz Stability of Ge…
This paper studies well-posedness and parameter sensitivity of the Square Root LASSO (SR-LASSO), an optimization model for recovering sparse solutions to linear inverse problems in finite dimension. An advantage of the SR-LASSO (e.g., over…
The Lasso and the basis pursuit in compressed sensing and machine learning are convex optimization problems with three parameters: the regularization scalar, the observation vector and the data matrix. Relative to the first two parameters,…
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…
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…
This paper addresses Lipschitzian stability issues that play an important role in both theoretical and numerical aspects of variational analysis, optimization, and their applications. We particularly concentrate on the so-called relaxed…
This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the…
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
This paper is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz-Slyozov-Wagner (LSW) system in the case when the initial data has compact support. The…
Dantzig selector (DS) and LASSO problems have attracted plenty of attention in statistical learning, sparse data recovery and mathematical optimization. In this paper, we provide a theoretical analysis of the sparse recovery stability of…
We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields…
The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of stability analysis or bilevel optimization. An example of such a Lipschitzian property…
This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
In mathematics, a super-resolution problem can be formulated as acquiring high-frequency data from low-frequency measurements. This extrapolation problem in the frequency domain is well-known to be unstable. We propose a model-based…
We study set-valued mappings defined by solution sets of parametric systems of equalities and inequalities. We prove Lipschitz-like continuity of these mappings under relaxed constant rank constraint qualification.
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal…
We consider a class of variable-exponent mixed fully nonlinear local and nonlocal degenerate elliptic equations, which degenerate along the set of critical points, $C:=\big\{x:\,Du(x)=0\big\}.$ Under general conditions, first, we establish…