Results 11  20
of
287
Solving LargeScale Sparse Semidefinite Programs for Combinatorial Optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1998
"... We present a dualscaling interiorpoint algorithm and show how it exploits the structure and sparsity of some large scale problems. We solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the first computational re ..."
Abstract

Cited by 119 (11 self)
 Add to MetaCart
(Show Context)
We present a dualscaling interiorpoint algorithm and show how it exploits the structure and sparsity of some large scale problems. We solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the first computational results of interiorpoint algorithms for approximating the maximum cut semidefinite programs with dimension upto 3000.
Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
, 1997
"... Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (IgDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (IgDM). In this paper, we follow the successful approach in [20] and solve the IgDMCP by ..."
Abstract

Cited by 82 (15 self)
 Add to MetaCart
Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (IgDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (IgDM). In this paper, we follow the successful approach in [20] and solve the IgDMCP by generalizing the completion problem to allow for approximate completions. In particular, we introduce a primaldual interiorpoint algorithm that solves an equivalent (quadratic objective function) semidefinite programming problem (SDP). Numerical results are included which illustrate the efficiency and robustness of our approach. Our randomly generated problems consistently resulted in low dimensional solutions when no completion existed.
Feedback Utilization Control in Distributed RealTime Systems with EndtoEnd Tasks
 IEEE Trans. Parallel and Distributed Systems
, 2005
"... Abstract—An increasing number of distributed realtime systems face the critical challenge of providing quality of service guarantees in open and unpredictable environments. In particular, such systems often need to enforce utilization bounds on multiple processors in order to avoid overload and mee ..."
Abstract

Cited by 80 (29 self)
 Add to MetaCart
(Show Context)
Abstract—An increasing number of distributed realtime systems face the critical challenge of providing quality of service guarantees in open and unpredictable environments. In particular, such systems often need to enforce utilization bounds on multiple processors in order to avoid overload and meet endtoend deadlines even when task execution times are unpredictable. While recent feedback control realtime scheduling algorithms have shown promise, they cannot handle the common endtoend task model where each task is comprised of a chain of subtasks distributed on multiple processors. This paper presents the Endtoend Utilization CONtrol (EUCON) algorithm that adaptively maintains desired CPU utilization through performance feedbacks loops. EUCON is based on a model predictive control approach that models utilization control on a distributed platform as a multivariable constrained optimization problem. A multiinputmultioutput model predictive controller is designed based on a difference equation model that describes the dynamic behavior of distributed realtime systems. Both control theoretic analysis and simulations demonstrate that EUCON can provide robust utilization guarantees when task execution times deviate from estimation or vary significantly at runtime. Index Terms—Realtime systems, embedded systems, distributed systems, feedback control realtime scheduling, endtoend task, quality of service, model predictive control. æ
Convex Nondifferentiable Optimization: A Survey Focussed On The Analytic Center Cutting Plane Method.
, 1999
"... We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a selfcontained convergence analysis, that uses the formalism of the theory of selfconcordant functions, but for the main results, we give direct pr ..."
Abstract

Cited by 75 (3 self)
 Add to MetaCart
We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a selfcontained convergence analysis, that uses the formalism of the theory of selfconcordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of two extensions that are very relevant to practical problems: the case of multiple cuts and the case of deep cuts. We further examine extensions to problems including feasible sets partially described by an explicit barrier function, and to the case of nonlinear cuts. Finally, we review several implementation issues and discuss some applications.
An interiorpoint method for largescale ℓ1regularized logistic regression
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2007
"... Recently, a lot of attention has been paid to ℓ1regularization based methods for sparse signal reconstruction (e.g., basis pursuit denoising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as ..."
Abstract

Cited by 74 (6 self)
 Add to MetaCart
Recently, a lot of attention has been paid to ℓ1regularization based methods for sparse signal reconstruction (e.g., basis pursuit denoising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as ℓ1regularized leastsquares programs (LSPs), which can be reformulated as convex quadratic programs, and then solved by several standard methods such as interiorpoint methods, at least for small and medium size problems. In this paper, we describe a specialized interiorpoint method for solving largescale ℓ1regularized LSPs that uses the preconditioned conjugate gradients algorithm to compute the search direction. The interiorpoint method can solve large sparse problems, with a million variables and observations, in a few tens of minutes on a PC. It can efficiently solve large dense problems, that arise in sparse signal recovery with orthogonal transforms, by exploiting fast algorithms for these transforms. The method is illustrated on a magnetic resonance imaging data set.
On Cones of Nonnegative Quadratic Functions
, 2001
"... We derive LMIcharacterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized copositivity. These matrix cones are in fact cones of nonconvex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for ..."
Abstract

Cited by 71 (15 self)
 Add to MetaCart
(Show Context)
We derive LMIcharacterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized copositivity. These matrix cones are in fact cones of nonconvex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for instance the intersection of a (upper) levelset of a quadratic function and a halfplane. We arrive at a generalization of Yakubovich's Sprocedure result. As an application we show that optimizing a general quadratic function over the intersection of an ellipsoid and a halfplane can be formulated as SDP, thus proving the polynomiality of this class of optimization problems, which arise, e.g., from the application of the trust region method for nonlinear programming. Other applications are in control theory and robust optimization. Keywords: LMI, SDP, CoPositive Cones, Quadratic Functions, SProcedure, Matrix Decomposition.
A superlinearly convergent predictorcorrector method for degenerate LCP in a wide neighborhood of the central path with O (√n L)iteration complexity
, 2006
"... ..."
Geometrydriven photorealistic facial expression synthesis
 In Symposium on Computer Animation
, 2003
"... ..."
(Show Context)
DEUCON: Decentralized EndtoEnd Utilization Control for Distributed RealTime Systems
 IEEE Trans. Parallel and Distributed Systems
, 2007
"... Abstract—Many realtime systems must control their CPU utilizations in order to meet endtoend deadlines and prevent overload. Utilization control is particularly challenging in distributed realtime systems with highly unpredictable workloads and a large number of endtoend tasks and processors. ..."
Abstract

Cited by 45 (16 self)
 Add to MetaCart
(Show Context)
Abstract—Many realtime systems must control their CPU utilizations in order to meet endtoend deadlines and prevent overload. Utilization control is particularly challenging in distributed realtime systems with highly unpredictable workloads and a large number of endtoend tasks and processors. This paper presents the Decentralized Endtoend Utilization CONtrol (DEUCON) algorithm, which can dynamically enforce the desired utilizations on multiple processors in such systems. In contrast to centralized control schemes adopted in earlier works, DEUCON features a novel decentralized control structure that requires only localized coordination among neighbor processors. DEUCON is systematically designed based on recent advances in distributed model predictive control theory. Both controltheoretic analysis and simulations show that DEUCON can provide robust utilization guarantees and maintain global system stability despite severe variations in task execution times. Furthermore, DEUCON can effectively distribute the computation and communication cost to different processors and tolerate considerable communication delay between local controllers. Our results indicate that DEUCON can provide a scalable and robust utilization control for largescale distributed realtime systems executing in unpredictable environments. Index Terms—Realtime and embedded systems, feedback control realtime scheduling, distributed systems, endtoend task, decentralized model predictive control. Ç 1