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On Shor's r-Algorithm for Problems with Constraints
Кібернетика та комп'ютерні технології, 2023 Introduction. Nonsmooth optimization problems arise in a wide range of applications, including engineering, finance, and deep learning, where activation functions often have discontinuous derivatives, such as ReLU.
Vladimir Norkin, Anton Kozyriev
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IEEE Access, 2022 Quaternions have appeared in many practical fields, such as image processing and data mining, and so on. This paper focuses on designing an efficient quaternion-valued neurodynamic approach (QNA) based on multi-agent systems to solve nonsmooth convex ...
Guocheng Li +3 more
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Use of the Shor’s r-Algorithm in Linear Robust Optimization Problems
Кібернетика та комп'ютерні технології, 2021 The paper is devoted to the description of a new approach to the construction of algorithms for solving linear programming problems (LP-problems), in which the number of constraints is much greater than the number of variables.
P. Stetsyuk +3 more
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GNU Octave and Python Implementation of Shor's r-Algorithm with Adaptive Step Control
Кібернетика та комп'ютерні технології, 2022 r-algorithms, or subgradient methods with dilation of space in the direction of the difference of two sequential subgradients, were proposed by N.Z.Shor in 1970 in his doctoral thesis. Respective software implementations proved to be competitive with the
Petro Stetsyuk +2 more
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Gradient-based Regularization Parameter Selection for Problems With Nonsmooth Penalty Functions [PDF]
Journal of Computational and Graphical Statistics, 2018 In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced.
Feng, Jean, Simon, Noah
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An Infeasible Bundle Method for Nonsmooth Convex Constrained Optimization without a Penalty Function or a Filter [PDF]
SIAM Journal on Optimization, 2005 From the abstract: In this paper, we demonstrate that the use of a parametrized penalty function in nonsmooth convex optimization can be avoided without using the relatively complex filter methods. We propose an approach which appears to be more direct and easier to implement, in the sense that it is closer in the spirit and structure to the well ...
Sagastizábal, Claudia, Solodov, Mikhail
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Generalized Nonconvex Nonsmooth Low-Rank Minimization [PDF]
, 2014 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 matrix recovery ...
Lin, Zhouchen +3 more
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Penalty-free method for nonsmooth constrained optimization via radial basis functions
TURKISH JOURNAL OF MATHEMATICS, 2017 Summary: We consider a general class of nonlinear constrained optimization problems, where derivatives of the objective function and constraints are unavailable. This property of problems can often impede the performance of optimization algorithms. Most algorithms usually determine a quasi-Newton direction and then use line search techniques.
Rahmanpour, Fardin +2 more
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A New Unified Path to Smoothing Nonsmooth Exact Penalty Function for the Constrained Optimization
Open Journal of Optimization, 2021 We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.
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Shape Parameter Estimation [PDF]
, 2017 Performance of machine learning approaches depends strongly on the choice of misfit penalty, and correct choice of penalty parameters, such as the threshold of the Huber function.
Aravkin, Aleksandr Y. +2 more
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