Related papers: Potentialities of Nonsmooth Optimization
This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the…
This paper is devoted to study of optimality conditions at infinity in nonsmooth minimax programming problems and applications. By means of the limiting subdifferential and normal cone at infinity, we dirive necessary and sufficient…
In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints…
We present a procedure to numerically compute finite step worst case performance guarantees on a given algorithm for the unconstrained optimization of strongly convex functions with Lipschitz continuous gradients. The solution method…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
In this paper, we first study nonsmooth steepest descent method for nonsmooth functions defined on Hilbert space and establish the corresponding algorithm by proximal subgradients. Then, we use this algorithm to find stationary points for…
We consider minimizing nonsmooth convex functions with bounded subgradients. However, instead of directly observing a subgradient at every step $k\in [0, \dots, N-1]$, we assume that the optimizer receives an adversarially corrupted…
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…
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional data observed under a fixed synchronous design over H\"older…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers. Using gH-differentiability of a fuzzy-valued function $\tilde{f}$, new necessary and sufficient optimality conditions are…
Exhausters are families of convex compact sets that allow one to represent directional derivative of the studied function at the considered point in the form of InfMax or SupMin of linear functions. Functions for which such a representation…
Motivated by the problem of the dynamics of point-particles in high post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a certain class of functions which are smooth except at some isolated points around which they…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear…
Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…
If the $n-th$ order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Hence, its order can be reduced to the lower order. In this paper,…