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In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phase, optimality is improved by means of the consideration of the objective function, on the tangent subspace to the constraints. In this paper, optimal assumptions are stated on the Restoration Phase and the Optimization Phase that establish the global convergence of the algorithm. Some numerical examples are also given by mixture problem and octagon problem.<\/jats:p>","DOI":"10.1155\/2010\/976529","type":"journal-article","created":{"date-parts":[[2010,12,8]],"date-time":"2010-12-08T19:36:10Z","timestamp":1291836970000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Two\u2010Phase Generalized Reduced Gradient Method for Constrained Global Optimization"],"prefix":"10.1155","volume":"2010","author":[{"given":"Abdelkrim","family":"El Mouatasim","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,12,8]]},"reference":[{"key":"e_1_2_7_1_2","first-page":"183","article-title":"Reduced gradient method for minimax estimation of a bounded Poisson mean","volume":"2","author":"El Mouatasim A.","year":"2009","journal-title":"Journal of Statistics: Advances in Theory and Applications"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.11.004"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.102"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/03052150701218475"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377\u20102217(81)90277\u20100"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0328048"},{"key":"e_1_2_7_7_2","first-page":"463","article-title":"Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization","volume":"16","author":"El Mouatasim A.","year":"2006","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"key":"e_1_2_7_8_2","series-title":"Nonconvex Optimization and Its Applications","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/978-1-4613-0251-3_29","volume-title":"Frontiers in Global Optimization","author":"Souza de Cursi J. 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