conic programming
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Author(s):  
Margarita P. Castro ◽  
Andre A. Cire ◽  
J. Christopher Beck




2021 ◽  
pp. ijoo.2019.0048
Author(s):  
Xin-Yee Lam ◽  
Defeng Sun ◽  
Kim-Chuan Toh

We first propose a semi-proximal augmented Lagrangian-based decomposition method to directly solve the primal form of a convex composite quadratic conic-programming problem with a primal block-angular structure. Using our algorithmic framework, we are able to naturally derive several well-known augmented Lagrangian-based decomposition methods for stochastic programming, such as the diagonal quadratic approximation method of Mulvey and Ruszczyński. Although it is natural to develop an augmented Lagrangian decomposition algorithm based on the primal problem, here, we demonstrate that it is, in fact, numerically more economical to solve the dual problem by an appropriately designed decomposition algorithm. In particular, we propose a semi-proximal symmetric Gauss–Seidel-based alternating direction method of multipliers (sGS-ADMM) for solving the corresponding dual problem. Numerical results show that our dual-based sGS-ADMM algorithm can very efficiently solve some very large instances of primal block-angular convex quadratic-programming problems. For example, one instance with more than 300,000 linear constraints and 12.5 million nonnegative variables is solved to the accuracy of 10-5 in the relative KKT residual in less than a minute on a modest desktop computer.





2021 ◽  
Vol 68 (1) ◽  
pp. 496-500
Author(s):  
Wenhao Jia ◽  
Tao Ding ◽  
Ming Qu ◽  
Linquan Bai ◽  
Fangxing Li
Keyword(s):  


2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yun Wang ◽  
Dezhou Kong

This paper considers the nonlinear symmetric conic programming (NSCP) problems. Firstly, a type of strong sufficient optimality condition for NSCP problems in terms of a linear-quadratic term is introduced. Then, a sufficient condition of the nonsingularity of Clarke’s generalized Jacobian of the Karush–Kuhn–Tucker (KKT) system is demonstrated. At last, as an application, this property is used to obtain the local convergence properties of a sequential quadratic programming- (SQP-) type method.





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