On the Fritz John saddle point problem for differentiable multiobjective optimization

OPSEARCH ◽  
2016 ◽  
Vol 53 (4) ◽  
pp. 917-933
Author(s):  
Maria C. Maciel ◽  
Sandra A. Santos ◽  
Graciela N. Sottosanto
Keyword(s):  
Multiobjective Optimization ◽  
Saddle Point ◽  
Saddle Point Problem ◽  
Point Problem

scholarly journals Computational aspects of the weak micro‐periodicity saddle point problem

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Ritukesh Bharali ◽  
Fredrik Larsson ◽  
Ralf Jänicke
Keyword(s):  
Saddle Point ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Computational Aspects

Accelerated Methods for Saddle-Point Problem

2020 ◽  
Vol 60 (11) ◽  
pp. 1787-1809
Author(s):  
M. S. Alkousa ◽  
A. V. Gasnikov ◽  
D. M. Dvinskikh ◽  
D. A. Kovalev ◽  
F. S. Stonyakin
Keyword(s):  
Saddle Point ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Accelerated Methods

scholarly journals Numerical solutions of symmetric saddle point problem by direct methods

2013 ◽  
Vol 46 (3) ◽  
Author(s):  
Alicja Smoktunowicz ◽  
Felicja Okulicka-Dłużewska
Keyword(s):  
Saddle Point ◽  
Numerical Solutions ◽  
Direct Methods ◽  
Qr Decomposition ◽  
Saddle Point Problem ◽  
Singular Value ◽  
Point Problem ◽  
Numerical Comparison ◽  
Augmented System ◽  
Value Decomposition

AbstractNumerical stability of two main direct methods for solving the symmetric saddle point problem are analyzed. The first one is a generalization of Golub’s method for the augmented system formulation (ASF) and uses the Householder QR decomposition. The second method is supported by the singular value decomposition (SVD). Numerical comparison of some direct methods are given.

On first-order algorithms for l1/nuclear norm minimization

Acta Numerica ◽  
2013 ◽  
Vol 22 ◽  
pp. 509-575 ◽  
Author(s):  
Yurii Nesterov ◽  
Arkadi Nemirovski
Keyword(s):  
Saddle Point ◽  
Gradient Methods ◽  
Saddle Point Problem ◽  
Optimization Techniques ◽  
Nuclear Norm ◽  
Point Problem ◽  
Nuclear Norm Minimization ◽  
Dantzig Selector ◽  
First Order ◽  
Norm Minimization

In the past decade, problems related to l1/nuclear norm minimization have attracted much attention in the signal processing, machine learning and optimization communities. In this paper, devoted to l1/nuclear norm minimization as ‘optimization beasts’, we give a detailed description of two attractive first-order optimization techniques for solving problems of this type. The first one, aimed primarily at lasso-type problems, comprises fast gradient methods applied to composite minimization formulations. The second approach, aimed at Dantzig-selector-type problems, utilizes saddle-point first-order algorithms and reformulation of the problem of interest as a generalized bilinear saddle-point problem. For both approaches, we give complete and detailed complexity analyses and discuss the application domains.

Bang–bang property for an uncertain saddle point problem

2014 ◽  
Vol 28 (3) ◽  
pp. 605-613 ◽  
Author(s):  
Yun Sun ◽  
Yuanguo Zhu
Keyword(s):  
Saddle Point ◽  
Saddle Point Problem ◽  
Point Problem
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