On Some Recent Advances and Applications of D.C. Optimization

We review some recent advances of d.c. optimization methods in the analysis and solution of specially structured nonconvex optimization problems, including problems from continuous location, nonconvex quadratic programming and monotonic optimization.

[1]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[2]  Faiz A. Al-Khayyal,et al.  A D.C. optimization method for single facility location problems , 1995, J. Glob. Optim..

[3]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[4]  B. Jaumard,et al.  WEBER'S PROBLEM WITH ATTRACTION AND REPULSION , 1991 .

[5]  Hoang Tuy,et al.  D.C. Optimization: Theory, Methods and Algorithms , 1995 .

[6]  P. Apkarian,et al.  Robust control via concave minimization local and global algorithms , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[7]  Pierre Hansen,et al.  Global Optimization in Location , 1995 .

[8]  Stephen P. Boyd,et al.  A primal—dual potential reduction method for problems involving matrix inequalities , 1995, Math. Program..

[9]  Christodoulos A. Floudas,et al.  A Global Optimization Method For Weber’s Problem With Attraction And Repulsion , 1994 .

[10]  W. Hager,et al.  Large Scale Optimization : State of the Art , 1993 .

[11]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[12]  E. Saff,et al.  Distributing many points on a sphere , 1997 .

[13]  Robert H. Leary,et al.  Global Optima of Lennard-Jones Clusters , 1997, J. Glob. Optim..

[14]  Masakazu Kojima,et al.  Semidefinite Programming Relaxation for Nonconvex Quadratic Programs , 1997, J. Glob. Optim..

[15]  Hiroshi Konno,et al.  Multiplicative Programming Problems , 1995 .

[16]  Mahmut Parlar,et al.  Technical Note - Algorithms for Weber Facility Location in the Presence of Forbidden Regions and/or Barriers to Travel , 1994, Transp. Sci..

[17]  Hanif D. Sherali,et al.  A reformulation-convexification approach for solving nonconvex quadratic programming problems , 1995, J. Glob. Optim..

[18]  Christodoulos A. Floudas,et al.  αBB: A global optimization method for general constrained nonconvex problems , 1995, J. Glob. Optim..

[19]  Reuven Chen,et al.  Conditional Minisum and Minimax Location-Allocation Problems in Euclidean Space , 1988, Transp. Sci..

[20]  H. Tuy Convex analysis and global optimization , 1998 .

[21]  Jacques-François Thisse,et al.  An Algorithm for a Constrained Weber Problem , 1982 .

[22]  G. L. Xue,et al.  Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters , 1997, J. Glob. Optim..

[23]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[24]  Hanif D. Sherali,et al.  New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems , 1997, Oper. Res. Lett..

[25]  Hoang Tuy A General D.C. Approach to Location Problems , 1996 .

[26]  FAIZ A. AL-KHAYYAL,et al.  A relaxation method for nonconvex quadratically constrained quadratic programs , 1995, J. Glob. Optim..

[27]  Reuven Chen Solution of minisum and minimax location–allocation problems with Euclidean distances , 1983 .

[28]  Phan Thien Thach D.c. sets, d.c. functions and nonlinear equations , 1993, Math. Program..

[29]  P. T. Thach,et al.  Optimization on Low Rank Nonconvex Structures , 1996 .

[30]  Hoang Tuy,et al.  On nonconvex optimization problems with separated nonconvex variables , 1992, J. Glob. Optim..