IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v202y2024i3d10.1007_s10957-024-02503-5.html
   My bibliography  Save this article

Continuous Equality Knapsack with Probit-Style Objectives

Author

Listed:
  • Jamie Fravel

    (Virginia Tech)

  • Robert Hildebrand

    (Virginia Tech)

  • Laurel Travis

    (Virginia Tech)

Abstract

We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function.

Suggested Citation

  • Jamie Fravel & Robert Hildebrand & Laurel Travis, 2024. "Continuous Equality Knapsack with Probit-Style Objectives," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1060-1076, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02503-5
    DOI: 10.1007/s10957-024-02503-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02503-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-024-02503-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    2. Liping Zhang, 2013. "A Newton-Type Algorithm for Solving Problems of Search Theory," Advances in Operations Research, Hindawi, vol. 2013, pages 1-7, January.
    3. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    4. Kurt M. Bretthauer & Bala Shetty, 1995. "The Nonlinear Resource Allocation Problem," Operations Research, INFORMS, vol. 43(4), pages 670-683, August.
    5. 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.
    6. Patriksson, Michael & Strömberg, Christoffer, 2015. "Algorithms for the continuous nonlinear resource allocation problem—New implementations and numerical studies," European Journal of Operational Research, Elsevier, vol. 243(3), pages 703-722.
    7. Michael H. Rothkopf, 1969. "A Model of Rational Competitive Bidding," Management Science, INFORMS, vol. 15(7), pages 362-373, March.
    8. Cyrus Derman, 1959. "A Simple Allocation Problem," Management Science, INFORMS, vol. 5(4), pages 453-459, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jungho Park & Hadi El-Amine & Nevin Mutlu, 2021. "An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1213-1228, July.
    2. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    3. De Waegenaere, A.M.B. & Wielhouwer, J.L., 2001. "A Partial Ranking Algorithm for Resource Allocation Problems," Other publications TiSEM 8b2e0185-36f9-43df-8a3d-d, Tilburg University, School of Economics and Management.
    4. De Waegenaere, A.M.B. & Wielhouwer, J.L., 2001. "A Partial Ranking Algorithm for Resource Allocation Problems," Discussion Paper 2001-40, Tilburg University, Center for Economic Research.
    5. Kameshwaran, S. & Narahari, Y., 2009. "Nonconvex piecewise linear knapsack problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 56-68, January.
    6. Zhang, Bin & Hua, Zhongsheng, 2008. "A unified method for a class of convex separable nonlinear knapsack problems," European Journal of Operational Research, Elsevier, vol. 191(1), pages 1-6, November.
    7. Hoto, R.S.V. & Matioli, L.C. & Santos, P.S.M., 2020. "A penalty algorithm for solving convex separable knapsack problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    8. Chernonog, Tatyana & Goldberg, Noam, 2018. "On the multi-product newsvendor with bounded demand distributions," International Journal of Production Economics, Elsevier, vol. 203(C), pages 38-47.
    9. AgralI, Semra & Geunes, Joseph, 2009. "Solving knapsack problems with S-curve return functions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 605-615, March.
    10. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    11. Patriksson, Michael & Strömberg, Christoffer, 2015. "Algorithms for the continuous nonlinear resource allocation problem—New implementations and numerical studies," European Journal of Operational Research, Elsevier, vol. 243(3), pages 703-722.
    12. 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.
    13. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    14. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    15. Bretthauer, Kurt M. & Ross, Anthony & Shetty, Bala, 1999. "Nonlinear integer programming for optimal allocation in stratified sampling," European Journal of Operational Research, Elsevier, vol. 116(3), pages 667-680, August.
    16. DePaolo, Concetta A. & Rader, David Jr., 2007. "A heuristic algorithm for a chance constrained stochastic program," European Journal of Operational Research, Elsevier, vol. 176(1), pages 27-45, January.
    17. Vogel, Sebastian & Meyr, Herbert, 2015. "Decentral allocation planning in multi-stage customer hierarchies," European Journal of Operational Research, Elsevier, vol. 246(2), pages 462-470.
    18. Calinescu, Melania & Bhulai, Sandjai & Schouten, Barry, 2013. "Optimal resource allocation in survey designs," European Journal of Operational Research, Elsevier, vol. 226(1), pages 115-121.
    19. Bueno, L.F. & Haeser, G. & Kolossoski, O., 2024. "On the paper “Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem”," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1217-1222.
    20. Torrealba, E.M.R. & Silva, J.G. & Matioli, L.C. & Kolossoski, O. & Santos, P.S.M., 2022. "Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 46-59.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02503-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.