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On methods for solving nonlinear semidefinite optimization problems

Jie Sun
2011 Numerical Algebra, Control and Optimization  
In particular, we discuss first and second-order algorithms that appear to be promising, which include the alternating direction method, the augmented Lagrangian method, and the smoothing Newton method  ...  However, much work is yet to be done to effectively solve this problem. We introduce some new theoretical and algorithmic development in this field.  ...  This research is partially supported by a Provost's Chair Professorship at National University of Singapore.  ... 
doi:10.3934/naco.2011.1.1 fatcat:s7cg76fenjh43i6n2hcw5o6ake

Page 667 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
Then they apply a certain Newton-type method to solve inexactly the smooth equations, with the smooth approximation refined after each Newton iteration, until a solution of desired accuracy for the original  ...  The semidefinite complementarity problem (SDCP) (i.e., comple- mentarity problems defined over the cone of symmetric positive semidefinite real matrices) is a generalization of several optimiza- tion problems  ... 

A semi-smooth Newton method for solving convex quadratic programming problem under simplicial cone constraint [article]

J. G. Barrios, O. P. Ferreira, S. Z. Németh
2015 arXiv   pre-print
It is shown that a semi-smooth Newton method applied to this nonsmooth system of equations is always well defined and under a mild assumption on the simplicial cone the method generates a sequence that  ...  In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem.  ...  This paper is a continuation of [13] , where we studied the problem of projection onto a simplicial cone by using a semi-smooth Newton method.  ... 
arXiv:1503.02753v1 fatcat:v6hvhsrof5dbbj5sjely2em2zy

Page 8701 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
The previous algo- rithm mainly uses the generalized Newton method, and adopts a homotopy algorithm for the smoothing mapping (not the origi- nal mapping F ) when the generalized Newton method fails.  ...  Most of the existing solution methods for MCP, such as the generalized New- ton method and the smoothing method, require monotonicity or the Py property of the mapping involved in MCP for global con- vergence  ... 

A one-step smoothing Newton method for second-order cone programming

Xiaoni Chi, Sanyang Liu
2009 Journal of Computational and Applied Mathematics  
Based on this new function, a one-step smoothing Newton method is presented for solving the second-order cone programming.  ...  A new smoothing function for the second-order cone programming is given by smoothing the symmetric perturbed Fischer-Burmeister function.  ...  Acknowledgements The authors are grateful to the associate editor and the referees for their valuable comments on the paper. We thank some of the pioneers of the smoothing Newton method field: J.  ... 
doi:10.1016/ fatcat:z5pwikfyqnfnrixvtkg2ynzbie

A smoothing method for second order cone complementarity problem

Xiangsong Zhang, Sanyang Liu, Zhenhua Liu
2009 Journal of Computational and Applied Mathematics  
Based on a perturbed symmetrically smoothing function, which has coerciveness under proper conditions, we present a smoothing Newton method for this problem.  ...  In this paper, the second order cone complementarity problem is studied.  ...  Acknowledgements The authors thank some of the pioneers of the smoothing Newton method field: L. Qi, D. Sun, J. Sun and Z. Huang etc.  ... 
doi:10.1016/ fatcat:inu63yrac5ghhohynlayn2ruhi

CALIPSO: A Differentiable Solver for Trajectory Optimization with Conic and Complementarity Constraints [article]

Taylor A. Howell, Simon Le Cleac'h, Kevin Tracy, Zachary Manchester
2022 arXiv   pre-print
We present a new solver for non-convex trajectory optimization problems that is specialized for robotics applications.  ...  CALIPSO, or the Conic Augmented Lagrangian Interior-Point SOlver, combines several strategies for constrained numerical optimization to natively handle second-order cones and complementarity constraints  ...  Acknowledgments The authors would like to thank Shane Barratt for helpful discussions related to cone programming.  ... 
arXiv:2205.09255v1 fatcat:5jqpfnc55be3dm5ocrpcruoqru

Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem

Y. Kanno, J. A. C. Martins, A. Pinto da Costa
2005 International Journal for Numerical Methods in Engineering  
The equilibrium configurations are obtained by using a combined smoothing and regularization method for the second-order cone complementarity problem. of the LCP, and is a particular case of a semidefinite  ...  A new formulation is presented for the three-dimensional incremental quasi-static problems with unilateral frictional contact.  ...  Hayashi (Kyoto University, Japan) for having allowed the use of the software developed by them, which is an implementation of the algorithm proposed in [15] .  ... 
doi:10.1002/nme.1493 fatcat:z4hcm6uptrbpzmggar273kjwje

A smoothing Newton-type method for second-order cone programming problems based on a new smoothing Fischer-Burmeister function

Liang Fang, Zengzhe Feng
2011 Computational and Applied Mathemathics  
A new smoothing function of the well known Fischer-Burmeister function is given. Based on this new function, a smoothing Newton-type method is proposed for solving secondorder cone programming.  ...  This algorithm can start from an arbitrary point and it is Q-quadratically convergent under a mild assumption. Numerical results demonstrate the effectiveness of the algorithm.  ...  Math., Vol. 30, N. 3, 2011 572 A SMOOTHING NEWTON-TYPE METHOD FOR CONE PROGRAMMING PROBLEMS Comp. Appl.  ... 
doi:10.1590/s1807-03022011000300005 fatcat:isijjnutg5fyxctfiebzw3homq

Complementarity Problems Over Symmetric Cones: A Survey of Recent Developments in Several Aspects [chapter]

Akiko Yoshise
2011 International Series in Operations Research and Management Science  
The complementarity problem over a symmetric cone (that we call the Symmetric Cone Complementarity Problem, or the SCCP) has received much attention of researchers in the last decade.  ...  Most of studies done on the SCCP can be categorized into the three research themes, interior point methods for the SCCP, merit or smoothing function methods for the SCCP, and various properties of the  ...  Introduction The complementarity problem over a symmetric cone (that we call the Symmetric Cone Complementarity Problem, or the SCCP) has received much attention of researchers in the last decade.  ... 
doi:10.1007/978-1-4614-0769-0_12 fatcat:vvyr5v2usnhbhfor2gnvk5rieu

On merit functions for p-order cone complementarity problem

Xin-He Miao, Yu-Lin Chang, Jein-Shan Chen
2016 Computational optimization and applications  
These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.  ...  In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving  ...  During the past decade, there had active research and various methods for complementarity problems, which include the interior-point methods, the smoothing Newton methods, the semismooth Newton methods  ... 
doi:10.1007/s10589-016-9889-y fatcat:vxiyhk3gynhq3gvs3rid2abkke

Page 4335 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
Methods Oper. Res. 51 (2000), no. 3, 459-470. The author concentrates on a Newton-type method for solving variational inequality problems with inequality constraints.  ...  ; Goteborg) A new merit function and an SQP method for non-strictly monotone variational inequalities.  ... 

A New Inexact Non-Interior Continuation Algorithm for Second-Order Cone Programming

Liang Fang
Non-interior continuation method is one of the most popular and efficient methods for solving second-order cone programming partially due to its superior numerical performances.  ...  In this paper, a new smoothing form of the well-known Fischer-Burmeister function is given. Based on the new smoothing function, an inexact non-interior continuation algorithm is proposed.  ...  Conclusions Based on a new smoothing function, we give a new inexact non-interior continuation algorithm for SOCP problems.  ... 
doi:10.24297/jam.v16i0.8152 fatcat:n44dpznfmfawdk4oczjh2mdcla

A Semismooth Newton Method for Tensor Eigenvalue Complementarity Problem [article]

Zhongming Chen, Liqun Qi
2015 arXiv   pre-print
Furthermore, we propose a damped semismooth Newton method for tensor eigenvalue complementarity problem.  ...  In this paper, we consider the tensor eigenvalue complementarity problem which is closely related to the optimality conditions for polynomial optimization, as well as a class of differential inclusions  ...  When the nonnegative cones in (1) are replaced by a closed convex cone and its dual cone, TEiCP is called the cone eigenvalue complementarity problem for high-order tensors by Ling, He and Qi [22] .  ... 
arXiv:1510.08570v1 fatcat:3odj7hmyhbbwpavpvymeeceolq

Page 1204 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
{For the entire collection see MR 90j:90079.} 91b:90201 90C33 65K05 De Pierro, A. R. (BR-FRJ) Nonlinear relaxation methods for solving symmetric linear complementarity problems. J. Optim.  ...  In this paper the author presents a family of iterative algorithms for solving a symmetric linear complementarity problem. These algo- rithms are based on nonlinear relaxation methods.  ... 
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