Related papers: Initialization-Free Lie-Bracket Extremum Seeking i…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
For a map that is strictly but not strongly convex, model-based gradient extremum seeking has an eigenvalue of zero at the extremum, i.e., it fails at exponential convergence. Interestingly, perturbation-based model-free extremum seeking…
An adaptive regularization algorithm using high-order models is proposed for partially separable convexly constrained nonlinear optimization problems whose objective function contains non-Lipschitzian $\ell_q$-norm regularization terms for…
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
Newton-type methods are typically analyzed under Lipschitz continuity of the Hessian, an assumption that can fail for objectives with higher-order or polynomial growth. We introduce a class of nonlinearly preconditioned Newton methods that…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
This paper addresses the problem of stochastic optimization with decision-dependent uncertainty, a class of problems where the probability distribution of the uncertain parameters is influenced by the decision-maker's actions. While recent…
We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global…
In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…
Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing…
We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack.…
Despite the recent success of reinforcement learning in various domains, these approaches remain, for the most part, deterringly sensitive to hyper-parameters and are often riddled with essential engineering feats allowing their success. We…
We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…
For a control system two major issues can be considered: the stabilizability with respect to a given target, and the minimization of an integral functional (while the trajectories reach this target). Here we consider a problem where…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
Given a domain above a Lipschitz graph, we establish solvability results for strongly elliptic second-order systems in divergence-form, allowed to have lower-order (drift) terms, with $L^p$-boundary data for $p$ near $2$ (more precisely, in…
Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant…
First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…