Alternating Direction Method of Multipliers Prof S. Boyd EE364b,StanfordUniversity source: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers (Boyd, Parikh, Chu, Peleato, Eckstein) 1
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Multiplier methods: a survey 135. where the vector ~(y, c) ~ R m has coordinates given by y,(y, c) i = yt+c4′[hi[x(y, c)]], i = 1.
. m (14) 4′ is the first derivative of 4, and II’ll is the usual Euclidean norm.
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THE METHOD OF LAGRANGE MULTIPLIERS William F. Trench Andrew G. Cowles Distinguished Professor Emeritus Department of Mathematics Trinity University San Antonio, Texas, USA [email protected] This is a supplement to the author’s Introductionto Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the.
If we use the Lagrange multiplier method, the equations in (1) imply that 2x +2‚x = 0; 4y +2‚y = 0 and x2 +y2 ¡1 = 0. From the ﬂrst two equations, we must have either ‚ = ¡1 or ‚ = ¡2. If ‚ = ¡1, then y = 0, x = §1 and f(x;y) = 1. Similarly, if ‚ = ¡2, then y = §1, x = 0 and f(x;y) = 0.