Related papers: Geometric characterizations of Lipschitz stability…
We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…
Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary…
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative…
In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…
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 investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus…
We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We…
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
Tilt stability plays a pivotal role in understanding how local solutions of an optimization problem respond to small, targeted perturbations of the objective. Although quadratic bundles are a powerful tool for capturing second-order…
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…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…