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Inverse optimization for linearly constrained convex separable programming problems

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  • Zhang, Jianzhong
  • Xu, Chengxian

Abstract

In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with l1 and l2 norms. These inverse optimization problems are either linear programming when l1 norm is used in the formulation, or convex quadratic separable programming when l2 norm is used.

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  • Zhang, Jianzhong & Xu, Chengxian, 2010. "Inverse optimization for linearly constrained convex separable programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 671-679, February.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:671-679
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    1. Ron Dembo & Dan Rosen, 1999. "The practice of portfolio replication. A practical overview of forward and inverse problems," Annals of Operations Research, Springer, vol. 85(0), pages 267-284, January.
    2. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    3. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    4. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    5. Renato D. C. Monteiro & Ilan Adler, 1990. "An Extension of Karmarkar Type Algorithm to a Class of Convex Separable Programming Problems with Global Linear Rate of Convergence," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 408-422, August.
    6. Jianzhong Zhang & Mao Cai, 1998. "Inverse problem of minimum cuts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 51-58, February.
    7. Li, Han-Lin & Yu, Chian-Son, 1999. "A global optimization method for nonconvex separable programming problems," European Journal of Operational Research, Elsevier, vol. 117(2), pages 275-292, September.
    8. Scott Carr & William Lovejoy, 2000. "The Inverse Newsvendor Problem: Choosing an Optimal Demand Portfolio for Capacitated Resources," Management Science, INFORMS, vol. 46(7), pages 912-927, July.
    9. P. T. Sokkalingam & Ravindra K. Ahuja & James B. Orlin, 1999. "Solving Inverse Spanning Tree Problems Through Network Flow Techniques," Operations Research, INFORMS, vol. 47(2), pages 291-298, April.
    10. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
    11. Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    12. Bruce A. McCarl & Hayri Önal, 1989. "Linear Approximation Using MOTAD and Separable Programming: Should It Be Done?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 71(1), pages 158-166.
    13. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
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