On the central path for nonlinear semidefinite programming

L. M. Grana Drummond; Alfredo Noel Iusem; B. F. Svaiter

RAIRO - Operations Research (2010)

  • Volume: 34, Issue: 3, page 331-345
  • ISSN: 0399-0559

Abstract

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In this paper we study the well definedness of the central path associated to a given nonlinear (convex) semidefinite programming problem. Under standard assumptions, we establish that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point.The monotonic behavior of the logarithmic barrier and the objective function along the trajectory is also discussed. Finally, the existence and optimality of cluster points are established.

How to cite

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Grana Drummond, L. M., Iusem, Alfredo Noel, and Svaiter, B. F.. "On the central path for nonlinear semidefinite programming." RAIRO - Operations Research 34.3 (2010): 331-345. <http://eudml.org/doc/197844>.

@article{GranaDrummond2010,
abstract = { In this paper we study the well definedness of the central path associated to a given nonlinear (convex) semidefinite programming problem. Under standard assumptions, we establish that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point.The monotonic behavior of the logarithmic barrier and the objective function along the trajectory is also discussed. Finally, the existence and optimality of cluster points are established. },
author = {Grana Drummond, L. M., Iusem, Alfredo Noel, Svaiter, B. F.},
journal = {RAIRO - Operations Research},
keywords = {Nonlinear semidefinite programming; semidefinite programming; central path; logarithmic barrier function; convex programming.; nonlinear (convex) semidefinite programming},
language = {eng},
month = {3},
number = {3},
pages = {331-345},
publisher = {EDP Sciences},
title = {On the central path for nonlinear semidefinite programming},
url = {http://eudml.org/doc/197844},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Grana Drummond, L. M.
AU - Iusem, Alfredo Noel
AU - Svaiter, B. F.
TI - On the central path for nonlinear semidefinite programming
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 3
SP - 331
EP - 345
AB - In this paper we study the well definedness of the central path associated to a given nonlinear (convex) semidefinite programming problem. Under standard assumptions, we establish that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point.The monotonic behavior of the logarithmic barrier and the objective function along the trajectory is also discussed. Finally, the existence and optimality of cluster points are established.
LA - eng
KW - Nonlinear semidefinite programming; semidefinite programming; central path; logarithmic barrier function; convex programming.; nonlinear (convex) semidefinite programming
UR - http://eudml.org/doc/197844
ER -

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