Li, D. Zero duality gap for a class of nonconvex optimization problems. (English) Zbl 0829.90109 J. Optim. Theory Appl. 85, No. 2, 309-324 (1995). By an equivalent transformation using the \(p\)th power of the objective function and the constraint, a saddle point can be generated for a general class of nonconvex optimization problems. Zero duality gap is thus guaranteed when the primal-dual method is applied to the constructed equivalent form. Reviewer: D.Li (Shatin, Hong Kong) Cited in 3 ReviewsCited in 45 Documents MSC: 90C26 Nonconvex programming, global optimization Keywords:saddle points; nonconvex optimization; primal-dual method PDFBibTeX XMLCite \textit{D. Li}, J. Optim. Theory Appl. 85, No. 2, 309--324 (1995; Zbl 0829.90109) Full Text: DOI References: [1] Lasdon, L. S.,Optimization Theory for Large Systems, Macmillan Company, London, England, 1970. · Zbl 0224.90038 [2] Luenberger, D. G.,Linear and Nonlinear Programming, 2nd Edition, Addison-Wesley, Reading, Massachusetts, 1984. · Zbl 0571.90051 [3] Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, pp. 303–320, 1969. · Zbl 0174.20705 · doi:10.1007/BF00927673 [4] Bertsekas, D. P.,Multiplier Methods: A Survey, Automatica, Vol. 12, pp. 133–145, 1976. · Zbl 0321.49027 · doi:10.1016/0005-1098(76)90077-7 [5] Rockafellar, R. T.,The Multiplier Method of Hestenes and Powell Applied to Convex Programming, Journal of Optimization Theory and Applications, Vol. 12, pp. 555–562, 1973. · Zbl 0254.90045 · doi:10.1007/BF00934777 [6] Bertsekas, D. P.,Convexification Procedures and Decomposition Methods for Nonconvex Optimization Problems, Journal of Optimization Theory and Applications, Vol. 29, pp. 169–197, 1979. · Zbl 0389.90080 · doi:10.1007/BF00937167 [7] Tanikawa, A., andMukai, H.,A New Technique for Nonconvex Primal-Dual Decomposition of a Large-Scale Separable Optimization Problem, IEEE Transactions on Automatic Control, Vol. 30, pp. 133–143, 1985. · Zbl 0553.90087 · doi:10.1109/TAC.1985.1103899 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.