Related papers: Nonsmooth method for constrained optimization
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and $\ell_{2,1}$-norm regularized cases, these…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set $\{x \in \mathcal{X}: c(x) = 0\}$, where $\mathcal{X}$ is a closed convex subset of $\mathbb{R}^n$. We propose an exact penalty approach,…
This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This work introduces MADS-PIP, an efficient framework that integrates a penalty-interior point strategy into the mesh adaptive direct search (MADS) algorithm for solving nonsmooth blackbox optimization problems with general inequality and…
We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free boundary (to be determined). The novelty of this method…
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
This paper concerns a class of constrained optimization problems in which, the objective and constraint functions are both upper-$\mathcal{C}^2$. For such nonconvex and nonsmooth optimization problems, we develop an inexact moving balls…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…