An improved branch and bound algorithm for mixed integer nonlinear programs

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Abstract

This paper describes an improved branch and bound code for zero-one mixed integer nonlinear programs with convex objective functions and constraints. The code uses Lagrangian duality to obtain lower bounds. The code also uses early branching to avoid solving some subproblems to optimality. Computational results show substantial performance improvements on many problems.

References (23)

  • C.A. Floudas et al.

    Global optimum search for nonconvex NLP and MINLP problems

    Comps Chem. Engng

    (1989)
  • I.E. Grossmann

    Mixed-integer programming approach for the synthesis of integrated process flow-sheets

    Comps Chem. Engng

    (1985)
  • H.H. Hoang

    Topological optimization of networks: a nonlinear mixed integer model employing generalized Benders decomposition

    IEEE Trans. Autom. Control

    (1982)
  • T.L. Magnanati et al.

    Network design and transportation planning: models and algorithms

    Transport. Sci.

    (1984)
  • Gary R. Kocis et al.

    Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis

    Ind. Engng Chem. Res.

    (1988)
  • B. Gavish et al.

    An approach to the optimal positioning of a new product

    Mgmt Sci.

    (1983)
  • D.J. Laughhunn

    Quadratic binary programming with applications to capital-budgeting problems

    Ops Res.

    (1970)
  • J.C.T. Mao et al.

    An extension of Lawler and Bell's method of discrete optimization with examples from capital budgeting

    Mgmt Sci.

    (1968)
  • H.M. Weingartner

    Capital budgeting of interrelated projects

    Mgmt Sci.

    (1966)
  • Omprakash K. Gupta et al.

    Nonlinear integer programming algorithms: a survey

    OPSEARCH

    (1983)
  • Pierre Hansen

    Methods of nonlinear 0–1 programming

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    †

    Brian Borchers is an Assistant Professor of Mathematics at New Mexico Tech. He holds an M.S. and a Ph.D. in Mathematics from Rensselaer and a B.S. in Computer Science from Rensselaer. His research interests are primarily in algorithms for mathematical programming.

    §

    John E. Mitchell is an Assistant Professor of Mathematics at Rensselaer. He holds an M.S. and a Ph.D. in Operations Research from Cornell University and a B.A. (Hons) in Mathematics from Cambridge University. His research interests are in interior point methods, integer programming, nonlinear programming, and their applications.

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    Copyright © 1994 Published by Elsevier Ltd.