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Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound
For the zero-norm regularized problem, we verify that the penalty problem of its equivalent MPEC reformulation is a global exact penalty, which...
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Correction of nonmonotone trust region algorithm based on a modified diagonal regularized quasi-Newton method
In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the...
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Exact penalty method for knot selection of B-spline regression
This paper presents a new approach to selecting knots at the same time as estimating the B-spline regression model. Such simultaneous selection of...
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On solving a rank regularized minimization problem via equivalent factorized column-sparse regularized models
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can...
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An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization
This paper focuses on the minimization of a sum of a twice continuously differentiable function f and a nonsmooth convex function. An inexact...
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A Penalty-Free Infeasible Approach for a Class of Nonsmooth Optimization Problems Over the Stiefel Manifold
Inspired by penalty-free approaches for smooth optimization problems, we propose a sequential linearized proximal gradient method (SLPG) for a class...
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Regularized frictional contact problems with the interior point method
The aim of this paper is to present an algorithm to solve frictional contact problems by considering the Coulomb’s criterion. As it is known, the...
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Theoretical Aspects in Penalty Hyperparameters Optimization
Learning processes play an important role in enhancing understanding and analyzing real phenomena. Most of these methodologies revolve around solving...
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Levenberg–Marquardt method and partial exact penalty parameter selection in bilevel optimization
We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a...
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Stable Solution of a Quadratic Minimization Problem with a Nonuniformly Perturbed Operator by Applying a Regularized Gradient Method
AbstractA regularized gradient method is proposed for stable solution of a quadratic minimization problem under nonconventional information...
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Inexact penalty decomposition methods for optimization problems with geometric constraints
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with...
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A global exact penalty for rank-constrained optimization problem and applications
This paper considers a rank-constrained optimization problem where the objective function is continuously differentiable on a closed convex set....
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General-purpose preconditioning for regularized interior point methods
In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from...
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An Entropy-Regularized ADMM For Binary Quadratic Programming
We propose an entropy regularized splitting model using low-rank factorization for solving binary quadratic programming with linear inequality...
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An Adaptive Penalty Method for Inequality Constrained Minimization Problems
The primal-dual active set method is observed to be the limit of a sequence of penalty formulations. Using this perspective, we propose a penalty...
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An exact penalty approach for optimization with nonnegative orthogonality constraints
Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some...
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A novel low-light enhancement via fractional-order and low-rank regularized retinex model
Most of existing low-light image enhancement approaches either fail to consider fine parts of the image or fail to consider intensive noise. To...
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Convergence Analysis of a Power Penalty Approach for a Class of Nonlocal Double Phase Complementarity Systems
In the present paper, we consider a nonlinear complementarity problem (NCP, for short) with a nonlinear and nonhomogeneous partial differential...