Global Optimization with Polynomials and the Problem of Moments

@article{Lasserre2001GlobalOW,
  title={Global Optimization with Polynomials and the Problem of Moments},
  author={Jean B. Lasserre},
  journal={SIAM Journal on Optimization},
  year={2001},
  volume={11},
  pages={796-817}
}
We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : Rn → R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush–Kuhn–Tucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided. 
Highly Influential
This paper has highly influenced 235 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 1,716 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 1,114 extracted citations

1,717 Citations

050100150'01'04'08'12'16
Citations per Year
Semantic Scholar estimates that this publication has 1,717 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 18 references

Positive polynomials on compact semi-algebraic sets

  • M. Putinar
  • Ind. Univ. Math. J., 42
  • 1993
Highly Influential
6 Excerpts

The K-moment problem for compact semi-algebraic sets

  • K. Schmüdgen
  • Math. Ann., 289
  • 1991
Highly Influential
5 Excerpts

Squared functional systems and optimization problems

  • Y. Nesterov
  • High Performance Optimization, H. Frenk, K. Roos…
  • 2000
Highly Influential
4 Excerpts

Nondifferentiable Optimization and Polynomial Problems

  • N. Z. Shor
  • Kluwer, Dordrecht
  • 1998
Highly Influential
7 Excerpts

Recursiveness

  • R. E. Curto, L. A. Fialkow
  • positivity, and truncated moment problems…
  • 1991
Highly Influential
5 Excerpts

Quadratic optimization problems

  • N. Z. Shor
  • Soviet J. Comput. Systems Sci., 25
  • 1987
Highly Influential
7 Excerpts

The multidimensional moment problem and semi-groups

  • C. Berg
  • Moments in Mathematics, H.J. Landau, ed., AMS…
  • 1980
Highly Influential
7 Excerpts

Optimality Conditions and LMI Relaxations for 0-1 Programs

  • J. B. Lasserre
  • Tech. report 2000099,
  • 2000
Highly Influential
3 Excerpts

Hilbert’s 17th problem and best dual bounds in quadratic minimization

  • C. Ferrier
  • Cybernet. Systems Anal., 34
  • 1998
Highly Influential
3 Excerpts

Similar Papers

Loading similar papers…