?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4103%2F&rft.title=Convex+Optimization+via+Feedbacks&rft.creator=Kryazhimskiy%2C+A.V.&rft.description=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%2C+system's+velocities+are+formed+through+current+relaxations+of+the+initial+problem.+In+relaxed+problems%2C+the+initial+equality+constraint+is+replaced+by+a+scalar+equality+or+a+scalar+inequality+showing%2C+respectively%2C+directions+to+keep+or+non-increase+a+current+value+of+the+discrepancy.+The+first+(alpha-shifting)+feedback+minimizes+Lagrangians+for+current+relaxed+problems%2C+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%2C+and+%22immediate+solution%22+trajectories+having+proper+asymptotics+with+time+shrinking+to+zero+are+designed.&rft.publisher=WP-94-109&rft.date=1994-10&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4103%2F1%2FWP-94-109.pdf&rft.identifier=++Kryazhimskiy%2C+A.V.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1393.html%3E++(1994).++Convex+Optimization+via+Feedbacks.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-109+++++