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Nonlinear Programming $$\sum _i\sum _j c_{ij}x_ix_j, \ \forall \ (i,j)$$ ∑ i ∑ j c ij x i x j , ∀ ( i , j )

In: Combinatorial, Linear, Integer and Nonlinear Optimization Apps

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  • J. MacGregor Smith

    (University of Massachusetts)

Abstract

overview Nonlinear Programming (NLP) problems represent some of the most complex optimization problems. Especially when contrasted with LP problems which have dominated the literature in Operations Research. This is because some of the nice properties such as monotonicity and convexity in Linear Programming are not always possible with NLP problems, so many local optimal solutions will exist, not just a single global optimization one. Figure 5.1 illustrates an example problem and the usual local vs. global phenomenon.

Suggested Citation

  • J. MacGregor Smith, 2021. "Nonlinear Programming $$\sum _i\sum _j c_{ij}x_ix_j, \ \forall \ (i,j)$$ ∑ i ∑ j c ij x i x j , ∀ ( i , j )," Springer Optimization and Its Applications, in: Combinatorial, Linear, Integer and Nonlinear Optimization Apps, chapter 0, pages 179-230, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-75801-1_5
    DOI: 10.1007/978-3-030-75801-1_5
    as

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