The Search for the Maximum of a Polynomial

For a real polynomialf(X) ofKvariables the problem of finding maxX?RKf(X) is investigated by reducing it to that of searching for the real roots of the univariate polynomial F(z):=?j(z?f(?j)), where the product is extended over all the critical points ?joff(X). Employment of the Hermite method of separation of real solutions of an algebraic equation system permits one to construct along withF(z) its Sturm series, and to restore the coordinates of the corresponding critical point. The problem of finding the maxfin the set defined by the real polynomial inequalityG(X)?0 is also discussed.

• Publication year

  1998

• Venue

  Journal of symbolic computation

• Publication date

  1998-05-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1006/jsco.1997.0190
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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