Semidefinite Programming and its
Partial list: as at 29 Nov 2005
Semidefinite programming (SDP) problems are linear optimization problems over the cone of positive semidefinite symmetric matrices. They have a particular structure that makes their solution computationally tractable by interior-point methods. The last decade has seen dramatic advances in the theory and practice of SDP, stimulated in part by the realization that interior-point methods can be applied very effectively to this class of convex optimization problems.
One of the earliest applications of SDP was in linear matrix inequalities (LMI) arising from systems and control. It has since also found other engineering applications including structural optimization and signal processing. On another front, SDP is now a widely used tool in the relaxations of NP-hard combinatorial optimization problems. The success in solving SDP problems of moderate size has resulted in increased interest in higher order relaxations of combinatorial optimization problems. More recently, SDP has also found applications in polynomial programming where under certain mild assumptions, a sequence of increasing order of SDP relaxations can converge to a globally optimal solution. The modeling power of SDP has also led to a paradigm shift in modeling robustness in optimization problems with uncertain data.
The widespread applications of SDP have thus led to great demands on quality solvers for SDP, especially solvers for large-scale problems. Recent progress towards solving large-scale SDP problems include algorithms which avoid using standard interior-point methodology but are based on first-order gradient or non-smooth methods applied to some Lagrangian dual or nonlinear programming reformulations. In addition, several parallel implementations of interior-point methods as well as column generation-type algorithms have also been proposed. Another class of algorithms is based on interior-point methods but they solve the Newton equations by a preconditioned Krylov subspace iterative method.
The program will provide a forum for the exchange of ideas among researchers working in theory, applications, algorithms, and software development of SDP.
IMS Membership is not required for participation in above activities. For attendance at these activities, please complete the registration form (MSWord|PDF|PS) and fax it to us at (65) 6873 8292 or email it to us at email@example.com.
If you are an IMS member or are applying for IMS membership, you do not need to register for these activities.
The Institute for Mathematical Sciences invites applications for membership for participation in the above program. Limited funds to cover travel and living expenses are available to young scientists. Applications should be received at least three (3) months before the commencement of membership. Application form is available in (MSWord|PDF|PS) format for download.
For enquiries on scientific aspects of the program, please email Kim-Chuan Toh at firstname.lastname@example.org.