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Convexity and complexity in polynomial programming. (English) Zbl 0588.90070
Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 1569-1577 (1984).
[For the entire collection see Zbl 0553.00001.]
In this survey the author considers the problems of convex polynomial programming: minimize \(f_ 0(x)\) subject to \(f_ j(x)\leq 0\), \(j=1,...,m\), \(x\in R^ n\), where \(f_ j\), \(j=0,1,...,m\), are convex polynomials with integer coefficients. Bounds for solutions are presented and the complexity of the ellipsoid method is estimated.
Reviewer: R.Lepp

90C25 Convex programming
68Q25 Analysis of algorithms and problem complexity
90C11 Mixed integer programming
90C10 Integer programming