Related papers: Characterization of tilt stability via subgradient…
Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a…
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…
The symmetric low-rank matrix factorization serves as a building block in many learning tasks, including matrix recovery and training of neural networks. However, despite a flurry of recent research, the dynamics of its training via…
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict complementarity. In this paper we establish a condition of…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
In this paper, we focus on providing convergence guarantees for stochastic subgradient methods in minimizing nonsmooth nonconvex functions. We first investigate the global stability of a general framework for stochastic subgradient methods,…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
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…
We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvyatskiy, and Jiang (2023) that for nonsmooth Lipschitz…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
The paper utilizes H\"older graphical derivatives for characterizing H\"older strong subregularity, isolated calmness and sharp minimum. As applications, we characterize H\"older isolated calmness in linear semi-infinite optimization and…
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the…