?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%2F4196%2F&rft.title=A+Bundle+of+Method+for+Minimizing+a+Sum+of+Convex+Functions+with+Smooth+Weights&rft.creator=Kiwiel%2C+K.&rft.description=We+give+a+bundle+method+for+minimizing+a+(possibly+nondifferentiable+and+nonconvex)+function+h(z)+%3D+sum_%7Bi%3D1%7D%5Em+p_i(x)+f_i(x)+over+a+closed+convex+set+in+R%5En%2C+where+p_i+are+nonnegative+and+smooth+and+f_i+are+finite-valued+convex.+Such+functions+arise+in+certain+stochastic+programming+problems+and+scenario+analysis.+The+method+finds+search+directions+via+quadratic+programming%2C+using+a+polyhedral+model+of+h+that+involves+current+linearizations+of+p_i+and+polyhedral+models+of+f_i+based+on+their+accumulated+subgradients.+We+show+that+the+method+is+globally+convergent+to+stationary+points+of+h.+The+method+exploits+the+structure+of+h+and+hence+seems+more+promising+than+general-purpose+bundle+methods+for+nonconvex+minimization.&rft.publisher=WP-94-013&rft.date=1994-03&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4196%2F1%2FWP-94-013.pdf&rft.identifier=++Kiwiel%2C+K.++(1994).++A+Bundle+of+Method+for+Minimizing+a+Sum+of+Convex+Functions+with+Smooth+Weights.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-013+++++