相关论文: Proximal linearized iteratively reweighted least s…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving smooth nonconvex composite optimization problems with nonlinear $\cal K$-convex constraints, i.e., the constraints are convex with respect to…
Sparse Partial Least Squares (sPLS) is a common dimensionality reduction technique for data fusion, which projects data samples from two views by seeking linear combinations with a small number of variables with the maximum variance.…
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by…
Total least squares (TLS) is an effective method for solving linear equations with the situations, when noise is not just in observation matrices but also in mapping matrices. Moreover, the Tikhonov regularization is widely used in plenty…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible…
We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is…
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
We herein propose a variant of the projected inexact Levenberg--Marquardt method (ILMM) for solving constrained nonsmooth equations. Since the orthogonal projection onto the feasible set may be computationally expensive, we propose a local…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In…
In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with…
Motivated by localization problems such as cadastral maps refinements, we consider a generic Nonlinear Least Squares (NLS) problem of minimizing an aggregate squared fit across all nonlinear equations (measurements) with respect to the set…
This paper presents smoothing schemes for obtaining approximate stationary points of unconstrained or linearly-constrained composite nonconvex-concave min-max (and hence nonsmooth) problems by applying well-known algorithms to composite…