Related papers: A modified exact penalty approach for general cons…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
We consider a modification of the OMM energy functional which contains an $\ell^1$ penalty term in order to find a sparse representation of the low-lying eigenspace of self-adjoint operators. We analyze the local minima of the modified…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters…
In this paper, we propose sparsity-aware data-selective adaptive filtering algorithms with adjustable penalties. Prior work incorporates a penalty function into the cost function used in the optimization that originates the algorithms to…
We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the…
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to modern error bound theory. The goal is twofold. First, we…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
In this paper we study nonconvex penalization using Bernstein functions. Since the Bernstein function is concave and nonsmooth at the origin, it can induce a class of nonconvex functions for high-dimensional sparse estimation problems. We…
We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for…
We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…