Gradient-type method for minimization of nonsmooth penalty functions

Cybernetics ◽  
1989 ◽  
Vol 24 (4) ◽  
pp. 511-524
Author(s):  
Yu. M. Danilin
Keyword(s):  
Penalty Functions ◽  
Type Method ◽  
Gradient Type ◽  
Nonsmooth Penalty

scholarly journals An improved multi-step gradient-type method for large scale optimization

2011 ◽  
Vol 61 (11) ◽  
pp. 3312-3318 ◽  
Author(s):  
Mahboubeh Farid ◽  
Wah June Leong
Keyword(s):  
Large Scale ◽  
Large Scale Optimization ◽  
Type Method ◽  
Gradient Type ◽  
Scale Optimization

Numerical experiments on stochastic block proximal-gradient type method for convex constrained optimization involving coordinatewise separable problems

2019 ◽  
Vol 35 (3) ◽  
pp. 371-378
Author(s):  
PORNTIP PROMSINCHAI ◽  
NARIN PETROT ◽  
◽  
◽  
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Objective Functions ◽  
Constrained Optimization Problems ◽  
Type Method ◽  
Coordinate Descent Algorithm ◽  
Proximal Gradient Algorithm ◽  
Separable Problems ◽  
Gradient Type

In this paper, we consider convex constrained optimization problems with composite objective functions over the set of a minimizer of another function. The main aim is to test numerically a new algorithm, namely a stochastic block coordinate proximal-gradient algorithm with penalization, by comparing both the number of iterations and CPU times between this introduced algorithm and the other well-known types of block coordinate descent algorithm for finding solutions of the randomly generated optimization problems with regularization term.

A Gradient-Type Method and Applications

2018 ◽  
pp. 85-107
Author(s):  
Antonio André Novotny ◽  
Jan Sokołowski ◽  
Antoni Żochowski
Keyword(s):  
Type Method ◽  
Gradient Type

Method of nonsmooth penalty functions and the theory of extremum problems in Banach space

Cybernetics ◽  
1980 ◽  
Vol 15 (5) ◽  
pp. 712-718 ◽  
Author(s):  
V. V. Beresnev
Keyword(s):  
Banach Space ◽  
Penalty Functions ◽  
Extremum Problems ◽  
Nonsmooth Penalty

scholarly journals A new two-step gradient-type method for large-scale unconstrained optimization

2010 ◽  
Vol 59 (10) ◽  
pp. 3301-3307 ◽  
Author(s):  
Mahboubeh Farid ◽  
Wah June Leong ◽  
Malik Abu Hassan
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Type Method ◽  
Gradient Type ◽  
Large Scale Unconstrained Optimization

scholarly journals Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Mahboubeh Farid ◽  
Wah June Leong ◽  
Lihong Zheng
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Positive Definite ◽  
Numerical Results ◽  
Type Method ◽  
Variable Space ◽  
Secant Equation ◽  
Gradient Type ◽  
Diagonal Updating ◽  
Large Scale Unconstrained Optimization

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is justO(n). Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods.

scholarly journals A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Can Li
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Type Method ◽  
Unconstrained Optimization Problems ◽  
Feasible Direction Method ◽  
Gradient Type ◽  
Large Scale Unconstrained Optimization ◽  
Nonnegative Constraints

We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.

Lassoing eigenvalues

Biometrika ◽  
2020 ◽  
Vol 107 (2) ◽  
pp. 397-414 ◽  
Author(s):  
David E Tyler ◽  
Mengxi Yi
Keyword(s):  
Covariance Matrix ◽  
Penalty Function ◽  
Covariance Matrices ◽  
Penalty Functions ◽  
Sample Covariance Matrix ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Nonsmooth Penalty

Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

Sign in / Sign up

Export Citation Format

Share Document