Related papers: An exact penalty approach for optimization with no…
This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…
In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of $\mathcal{O}(|\log(\epsilon)|)$…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied to address the essential boundary condition $u\cdot n = g$…
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…
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact…
The last decade witnessed a rise in the importance of supervised learning applications involving {\em big data} and {\em big models}. Big data refers to situations where the amounts of training data available and needed causes difficulties…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
In this work, we propose the joint use of a mixed penalty-interior point method and direct search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
We propose and study a version of the DCA (Difference-of-Convex functions Algorithm) using the $\ell_1$ penalty function for solving nonsmooth DC optimization problems with nonsmooth DC equality and inequality constraints. The method…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
This paper proposes a distributed algorithm for a network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained problem…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…