Kryazhimskiy, A.V.
(1998).
*Convex optimization via feedbacks.*
SIAM Journal on Control and Optimization 37 (1) 278-302. 10.1137/S036301299528030X.

## Abstract

Three dynamical systems are associated with a problem of convex optimization in a finite-dimensional space. For system trajectories $x(t)$, the ratios $x(t)/t$ are, respectively, (i) solution tracking (staying within the solution set $X^0$), (ii) solution abandoning (reaching $X^0$ as time $t$ goes back to the initial instant), and (iii) solution approaching (approaching $X^0$ as time $t$ goes to infinity). The systems represent a closed control system with appropriate feedbacks. In typical cases, the structure of the trajectories is simple enough. For instance, for a problem of quadratic programming with linear and box constraints, solution-approaching dynamics are described by a piecewise-linear ODE with a finite number of polyhedral domains of linearity. Finding the order of visiting these domains yields an analytic resolution of the original problem; a detailed analysis is given for a particular example. A discrete-time approach is outlined. bAe

Item Type: | Article |
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Research Programs: | Dynamic Systems (DYN) |

Bibliographic Reference: | SIAM Journal of Control and Optimization; 37(1):278-302 |

Depositing User: | IIASA Import |

Date Deposited: | 15 Jan 2016 02:09 |

Last Modified: | 27 Aug 2021 17:16 |

URI: | https://pure.iiasa.ac.at/5376 |

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