期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 63, 期 7, 页码 1973-1986出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2760256
关键词
Dynamic optimization; interior-point method; time-varying optimization
资金
- NSF [CAREER-ECCS-1651433, IIS-1447470]
- ONR [N00014-12-1-0997]
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system for tracking the (time-varying) optimal solution with an asymptotically vanishing error. This dynamical system is composed of two terms: a correction term consisting of a continuous-time version of Newton's method, and a prediction term able to track the drift of the optimal solution by taking into account the time-varying nature of the objective and constraint functions. Using appropriately chosen time-varying slack and barrier parameters, we ensure that the solution to this dynamical system globally asymptotically converges to the optimal solution at an exponential rate. We illustrate the applicability of the proposed method in two applications: a sparsity promoting least squares problem and a collision-free robot navigation problem.
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