-

 

 

 




Optimization Online





 

Time-Varying Semidefinite Programs

Amir Ali Ahmadi (a_a_a***at***princeton.edu)
Bachir El Khadir (bkhadir***at***princeton.edu)

Abstract: We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the optimal value of the TV-SDP. Moreover, by using a Positivstellensatz on univariate polynomial matrices, we show that the best polynomial solution of a given degree to a TV-SDP can be found by solving a semidefinite program of tractable size. We also provide a sequence of dual problems which can be cast as SDPs and that give upper bounds on the optimal value of a TV-SDP (in maximization form). We prove that under a boundedness assumption, this sequence of upper bounds converges to the optimal value of the TV-SDP. Under the same assumption, we also show that the optimal value of the TV-SDP is attained. We demonstrate the efficacy of our algorithms on a maximum-flow problem with time-varying edge capacities, a wireless coverage problem with time-varying coverage requirements, and on bi-objective semidefinite optimization where the goal is to approximate the Pareto curve in one shot.

Keywords: Semidefinite programming, time-varying convex optimization, univariate polynomial matrices, Positivstellensatze, continuous linear programs, bi-objective optimization

Category 1: Infinite Dimensional Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Applications -- Science and Engineering (Basic Sciences Applications )

Citation: Department of ORFE, Princeton University, August 2018.

Download: [PDF]

Entry Submitted: 08/12/2018
Entry Accepted: 08/12/2018
Entry Last Modified: 12/01/2019

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society