# 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

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topGrana 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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