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A Review of Piecewise Linearization Methods

Author

Listed:
  • Ming-Hua Lin
  • John Gunnar Carlsson
  • Dongdong Ge
  • Jianming Shi
  • Jung-Fa Tsai

Abstract

Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

Suggested Citation

  • Ming-Hua Lin & John Gunnar Carlsson & Dongdong Ge & Jianming Shi & Jung-Fa Tsai, 2013. "A Review of Piecewise Linearization Methods," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, November.
    • Handle: RePEc:hin:jnlmpe:101376
    DOI: 10.1155/2013/101376
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    8. Bitencourt, Leonardo & Dias, Bruno & Soares, Tiago & Borba, Bruno & Quirós-Tortós, Jairo, 2023. "e-Carsharing siting and sizing DLMP-based under demand uncertainty," Applied Energy, Elsevier, vol. 330(PB).
    9. Nebuloni, Riccardo & Meraldi, Lorenzo & Bovo, Cristian & Ilea, Valentin & Berizzi, Alberto & Sinha, Snigdh & Tamirisakandala, Raviteja Bharadwaj & Raboni, Pietro, 2023. "A hierarchical two-level MILP optimization model for the management of grid-connected BESS considering accurate physical model," Applied Energy, Elsevier, vol. 334(C).

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