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- S Kuhlmann, M Marshall, KUHLMANN M MARSHALL
- 2002

Let K be the basic closed semi-algebraic set in R n defined by some finite set of polynomials S and T , the preordering generated by S. For K compact, f a polynomial in n variables nonnegative on K and real > 0, we have that f + ∈ T. In particular, the K-Moment Problem has a positive solution. In the present paper, we study the problem when K is not… (More)

- M. Marshall, M. MARSHALL
- 2003

Recently progress has been made in the development of algorithms for optimizing poly-nomials. The main idea being stressed is that of reducing the problem to an easier problem involving semidefinite programming [18]. It seems that in many cases the method dramatically outperforms other existing methods. The idea traces back to work of Shor [16][17] and is… (More)

- M. Marshall
- 2006

Natural sufficient conditions for a polynomial to have a local minimum at a point are considered. These conditions tend to hold with probability 1. It is shown that polynomials satisfying these conditions at each minimum point have nice presentations in terms of sums of squares. Applications are given to optimization on a compact set and also to global… (More)

The paper is a continuation of work initiated by the first two authors in [K–M]. Section 1 is introductory. In Section 2 we give new proofs of results of Scheiderer in [S1] [S2] in the compact case; see Corollaries 2.3, 2.4 and 2.5. The main tool in Section 2, Lemma 2.1, is also used in Section 3 where we continue the examination of the case n = 1 initiated… (More)

- Mehdi Ghasemi, Murray Marshall
- SIAM Journal on Optimization
- 2012

We make use of a result of Hurwitz and Reznick [8] [19], and a consequence of this result due to Fidalgo and Kovacec [5], to determine a new sufficient condition for a polynomial f ∈ R[X 1 ,. .. , X n ] of even degree to be a sum of squares. This result generalizes a result of Lasserre in [10] and a result of Fidalgo and Kovacec in [5], and it also… (More)

- M. Marshall, M. MARSHALL
- 2003

- F.-V. Kuhlmann, S. Kuhlmann, M. Marshall, M. Zekavat
- 2007

Let F be an ordered eld, v the unique nest valuation on F compatible with the ordering (so v(a) v(b) ii njbj jaj for some integer n 1), V the value group of v and the residue eld of v (so is archimedean) 5] 10] 19]. If F 0 is an ordered extension of F , then the nest valuation on F 0 compatible with the extended ordering is an extension of v which we denote… (More)

- M. MARSHALL
- 2008

We prove that if f (x, y) is a polynomial with real coefficients which is non-negative on the strip [0, 1] × R, then f (x, y) has a presentation of the form f (x, y) = k i=1 g i (x, y) 2 + j=1 h j (x, y) 2 x(1 − x), where the g i (x, y) and h j (x, y) are polynomials with real coefficients.

- M. Marshall
- 2004

real spectra [7, Chs. 6–8], also called spaces of signs [1, Ch. 3], arise naturally in the study of semialgebraic sets, more generally, in the study of constructible sets in the real spectrum of a commutative ring with 1. Let A denote the ring of all polynomial functions on V , where V ⊆ R n is an algebraic set. Consider f, g ∈ A to be equivalent if f and g… (More)

- Daniel Plaumann, Sebastian Krug, +4 authors Rainer Sinn
- 2008

Gewidmet meinen Eltern Marina und Michael Plaumann und meinem Onkel Peter Plaumann in tiefer Dankbarkeit Acknowledgements I would like to express my gratitude to my advisor Claus Scheiderer for the many ideas and insights into the topic that he shared with me, as well as for his constant encouragement. I am grateful for many interesting and helpful… (More)