Skip to main content
SpringerLink
Log in

RLT: A unified approach for discrete and continuous nonconvex optimization

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Adams, W.P. and H.D. Sherali. (1986). “A Tight Linearization and an Algorithm for Zero-One Quadratic Programs.” Management Science, 32(10), 1274–1290.

    Google Scholar 

  • Adams, W.P. and H.D. Sherali. (1990). “Linearization Strategies for a Class of Zero-One Mixed-Integer Programming Problems.” Operations Research, 38(2), 217–226.

    Article  Google Scholar 

  • Adams, W.P. and H.D. Sherali. (1993). “Mixed-Integer Bilinear Programming Problems.” Mathematical Programming, 59(3), 279–305.

    Article  Google Scholar 

  • Audet, C., P. Hansen, B. Jaumard, and C. Savard. (2000). “A Branch and Cut Algorithm for Nonconvex Quadratically Constrained Quadratic Programming.” Mathematical Programming, 87(Series A), 131–152.

    Google Scholar 

  • Balas, E. (1975). “Disjunctive Programming: Cutting Planes from Logical Conditions.” In O.L. Mangasarian, R.R. Meyer, and S.M. Robinson (Eds.), Nonlinear Programming, New York: Academic Press.

    Google Scholar 

  • Balas, E. (1985). “Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems.” SIAM Journal on Algebraic and Discrete Methods, 6, 466–485.

    Google Scholar 

  • Balas, E., S. Ceria, and G. Cornuejols. (1993). “A Lift-and-Project Cutting Plane Algorithm for Mixed 0-1 Programs.” Mathematical Programming, 58, 295–324.

    Article  Google Scholar 

  • Bazaraa, M.S. and H.D. Sherali. (1980). “Benders’ Partitioning Applied to a New Formulation of the Quadratic Assignment Problem.” Naval Research Logistics Quarterly, 27(1), 28–42.

    Google Scholar 

  • Lim, C. and H.D. Sherali. (2006a). “Convergence and Computational Analysis for Some Variable Target Value and Subgradient Deflection Methods.” Computational Optimization and Applications, 34(3), 409–428.

  • Lim, C. and H.D. Sherali. (2006b). “A Trust Region Target Value Method for Optimizing Nondifferentiable Lagrangian Duals of Linear Programs.” Mathematical Methods of Operations Research, 64, 33–53.

    Google Scholar 

  • Loiolla, E.M., N.M. Maia de Abren, P.O. Boaventura-Netto, P. Hahn, and T. Querido. (2004). An Analytical Survey for the Quadratic Assignment Problem. Pittsburgh, PA: University of Pennsylvania.

    Google Scholar 

  • Lovasz, L. and A. Schrijver. (1991). “Cones of Matrices and Set Functions and 0-1 Optimization.” SIAM Journal on Optimization, 1, 166–190.

    Article  Google Scholar 

  • Sahinidis, N.V. (1996). BARON: A General Purpose Global Optimization Software Package.” Journal of Global Optimization, 8(2), 201–205.

    Article  Google Scholar 

  • Sherali, H.D. and W.P. Adams. (1984). “A Decomposition Algorithm for a Discrete Location-Allocation Problem.” Operations Research, 32(4), 878–900.

    Google Scholar 

  • Sherali, H.D. and W.P. Adams. (1990). “A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems.” SIAM Journal on Discrete Mathematics, 3(3), 411–430.

    Article  Google Scholar 

  • Sherali, H.D. and W.P. Adams. (1994). “A Hierarchy of Relaxations and Convex Hull Characterizations for Mixed-Integer Zero-One Programming Problems.” Discrete Applied Mathematics, 52, 83–106.

    Article  Google Scholar 

  • Sherali, H.D. and W.P. Adams. (1999). A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems Dordrecht/Boston/London: Kluwer Academic Publishers.

    Google Scholar 

  • Sherali, H.D., W.P. Adams, and P.J. Driscoll. (1998). “Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems.” Operations Research, 46(3), 396–405.

    Google Scholar 

  • Sherali, H.D. and J. Desai. (2005). “On Solving Polynomial, Factorable, and Black-box Optimization Problems using the RLT Methodology.” In C. Audet, P. Hansen, and G. Savard (Eds.), Essays and Surveys on Global Optimization. New York, NY: Springer, pp. 131–163.

    Chapter  Google Scholar 

  • Sherali, H.D. and B.M.P. Fraticelli. (2002). “Enhancing RLT Relaxations Via a New Class of Semidefinite Cuts.” In special issue in honor of Professor Reiner Horst, P.M. Pardalos and N.V. Thoai (eds.), Journal of Global Optimization, 22(1–4), 233–261.

  • Sherali, H.D. and V. Ganesan. (2003). “A Pseudo-Global Optimization Approach with Application to the Design of Containerships.” Journal of Global Optimization, 26, 335–360.

    Article  Google Scholar 

  • Sherali, H.D. and D.C. Myers, (1988). “Dual Formulations and Subgradient Optimization Strategies for Linear Programming Relaxations of Mixed-Integer Programs.” Discrete Applied Mathematics, 20, 51–68.

    Article  Google Scholar 

  • Sherali, H.D. and C.M. Shetty. (1980). Optimization with Disjunctive Constraints, Berlin-Heidelberg-New York: Springer-Verlag, Series in Economics and Mathematical Systems, Publication Number 181.

  • Sherali, H.D. and C.H. Tuncbilek. (1992). “A Global Optimization Algorithm for Polynomial Programming Problems Using a Reformulation-Linearization Technique.” Journal of Global Optimization, 2, 101–112.

    Article  Google Scholar 

  • Sherali, H.D. and C.H. Tuncbilek. (1995). “A Reformulation-Convexification Approach for Solving Nonconvex Quadratic Programming Problems.” Journal of Global Optimization, 7, 1–31.

    Article  Google Scholar 

  • Sherali, H.D. and C.H. Tuncbilek. (1997). “New Reformulation-Linearization/Convexification Relaxations for Univariate and Multivariate Polynomial Programming Problems.” Operations Research Letters, 21(1), 1–10.

    Article  Google Scholar 

  • Sherali, H.D. and H. Wang. (2001). “Global Optimization of Nonconvex Factorable Programming Problems.” Mathematical Programming, 89(3), 459–478.

    Article  Google Scholar 

  • Vandenbussche, D. and G.L. Nemhauser. (2005). “A Branch-and-cut Algorithm for Nonconvex Quadratic Programs with Box Constraints.” Mathematical Programming, 102(3), 559–576.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Grado Department of Industrial and Systems Engineering, Virginia Tech, 250 Durham Hall (0118), Blacksburg, Virginia, 24061, USA

    Hanif D. Sherali

Authors
  1. Hanif D. Sherali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hanif D. Sherali.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sherali, H.D. RLT: A unified approach for discrete and continuous nonconvex optimization. Ann Oper Res 149, 185–193 (2007). https://doi.org/10.1007/s10479-006-0107-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-006-0107-7

Keywords

Search

Navigation