eprintid: 4103 rev_number: 20 eprint_status: archive userid: 351 dir: disk0/00/00/41/03 datestamp: 2016-01-15 02:04:06 lastmod: 2021-08-27 17:14:46 status_changed: 2016-01-15 02:04:06 type: monograph metadata_visibility: show item_issues_count: 3 creators_name: Kryazhimskiy, A.V. creators_id: 1514 title: Convex Optimization via Feedbacks ispublished: pub internal_subjects: iis_cmp internal_subjects: iis_met internal_subjects: iis_sys divisions: prog_dyn abstract: A method to approach a solution to a finite-dimensional convex optimization problem via trajectories of a control system is suggested. The feedbacks exploit the idea of extremal shifting control from the theory of closed-loop differential games. Under these feedbacks, system's velocities are formed through current relaxations of the initial problem. In relaxed problems, the initial equality constraint is replaced by a scalar equality or a scalar inequality showing, respectively, directions to keep or non-increase a current value of the discrepancy. The first (alpha-shifting) feedback minimizes Lagrangians for current relaxed problems, and results in a dynamical implementation of the penalty method. The second (half-space shifting) feedback solves relaxed problems directly. The first feedback is simpler but less accurate (accuracy bounds are pointed out). The sought solutions are approximated by state-over-time ratios. Discrete and continuous control patterns are considered. Asymptotical convergence with time growing to infinity is proved, and "immediate solution" trajectories having proper asymptotics with time shrinking to zero are designed. date: 1994-10 date_type: published publisher: WP-94-109 iiasapubid: WP-94-109 price: 10 creators_browse_id: 1393 full_text_status: public monograph_type: working_paper place_of_pub: IIASA, Laxenburg, Austria pages: 30 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Kryazhimskiy, A.V. (1994). Convex Optimization via Feedbacks. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-94-109 document_url: https://pure.iiasa.ac.at/id/eprint/4103/1/WP-94-109.pdf