-
2
-
-
0001559061
-
A quadratic form representation of polynomials of several variables and its applications
-
[BL68]
-
[BL68] Bose, N.K., Li, C.C.: A quadratic form representation of polynomials of several variables and its applications. IEEE Transactions on Automatic Control 14, 447-448 (1968)
-
(1968)
IEEE Transactions on Automatic Control
, vol.14
, pp. 447-448
-
-
Bose, N.K.1
Li, C.C.2
-
4
-
-
0030291482
-
On the combinatorial and algebraic complexity of quantifier elimination
-
[BPR96]
-
[BPR96] Basu, S., Pollack, R., Roy, M.-F.: On the combinatorial and algebraic complexity of quantifier elimination. J. ACM 43(6), 1002-1045 (1996)
-
(1996)
J. ACM
, vol.43
, Issue.6
, pp. 1002-1045
-
-
Basu, S.1
Pollack, R.2
Roy, M.-F.3
-
5
-
-
0001259424
-
Bounds for the degrees in the Nullstellensatz
-
[Bro87]
-
[Bro87] Brownawell, W.D.: Bounds for the degrees in the Nullstellensatz. Annals of Mathematics 126, 577-591 (1987)
-
(1987)
Annals of Mathematics
, vol.126
, pp. 577-591
-
-
Brownawell, W.D.1
-
6
-
-
0000892961
-
Recent improvements in the complexity of the effective Nullstellensatz
-
[BS91]
-
[BS91] Berenstein, C.A., Struppa, D.C.: Recent improvements in the complexity of the effective Nullstellensatz. Linear Algebra and its Applications 157(2), 203-215 (1991)
-
(1991)
Linear Algebra and its Applications
, vol.157
, Issue.2
, pp. 203-215
-
-
Berenstein, C.A.1
Struppa, D.C.2
-
8
-
-
0003908675
-
-
[CLO97]. Springer
-
[CLO97] Cox, D.A., Little, J.B., O'Shea, D.: Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra. Springer, 1997
-
(1997)
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
-
-
Cox, D.A.1
Little, J.B.2
O'Shea, D.3
-
9
-
-
0000082954
-
Sums of squares of real polynomials
-
[CLR95]
-
[CLR95] Choi, M.D., Lam, T.Y., Reznick, B.: Sums of squares of real polynomials. Proceedings of Symposia in Pure Mathematics 58(2), 103-126 (1995)
-
(1995)
Proceedings of Symposia in Pure Mathematics
, vol.58
, Issue.2
, pp. 103-126
-
-
Choi, M.D.1
Lam, T.Y.2
Reznick, B.3
-
11
-
-
0002106815
-
On non-negative forms in real variables some or all of which are non-negative
-
[Dia62]
-
[Dia62] Diananda, P.H.: On non-negative forms in real variables some or all of which are non-negative. Proceedings of the Cambridge Philosophical Society 58, 17-25 (1962)
-
(1962)
Proceedings of the Cambridge Philosophical Society
, vol.58
, pp. 17-25
-
-
Diananda, P.H.1
-
12
-
-
0036433723
-
Approximating the stability number of a graph via copositive programming
-
[dKP02]
-
[dKP02] de Klerk, E., Pasechnik, D.V.: Approximating the stability number of a graph via copositive programming. SIAM J. Optim. 12(4), 875-892 (2002)
-
(2002)
SIAM J. Optim.
, vol.12
, Issue.4
, pp. 875-892
-
-
De Klerk, E.1
Pasechnik, D.V.2
-
13
-
-
0003053246
-
Hilbert's 17th problem and best dual bounds in quadratic minimization
-
[Fer98]
-
[Fer98] Ferrier, Ch.: Hilbert's 17th problem and best dual bounds in quadratic minimization. Cybernetics and Systems Analysis 34(5), 696-709 (1998)
-
(1998)
Cybernetics and Systems Analysis
, vol.34
, Issue.5
, pp. 696-709
-
-
Ferrier, Ch.1
-
14
-
-
0032186918
-
Comments on A procedure for the positive definiteness of forms of even order
-
[Fu98]
-
[Fu98] Fu, M.: Comments on A procedure for the positive definiteness of forms of even order. IEEE Transactions on Automatic Control 43(10), 1430 (1998)
-
(1998)
IEEE Transactions on Automatic Control
, vol.43
, Issue.10
, pp. 1430
-
-
Fu, M.1
-
15
-
-
1542325670
-
-
[GP01]. Submitted, available from arXiv:math.AC/0211450
-
[GP01] Gatermann, K., Parrilo, P.A.: Symmetry groups, semidefinite programs, and sums of squares. Submitted, available from arXiv:math.AC/0211450, 2002
-
(2002)
Symmetry Groups, Semidefinite Programs, and Sums of Squares
-
-
Gatermann, K.1
Parrilo, P.A.2
-
16
-
-
0035960943
-
Complexity of Null- And positivstellensatz proofs
-
[GV02]
-
[GV02] Grigoriev, D., Vorobjov, N.: Complexity of Null- and Positivstellensatz proofs. Annals of Pure and Applied Logic 113(1-3), 153-160 (2002)
-
(2002)
Annals of Pure and Applied Logic
, vol.113
, Issue.1-3
, pp. 153-160
-
-
Grigoriev, D.1
Vorobjov, N.2
-
17
-
-
84893574327
-
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
-
[GW95]
-
[GW95] Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6), 1115-1145 (1995)
-
(1995)
J. ACM
, vol.42
, Issue.6
, pp. 1115-1145
-
-
Goemans, M.X.1
Williamson, D.P.2
-
18
-
-
0030127026
-
A procedure for the positive definiteness of forms of even order
-
[HH96]
-
[HH96] Hasan, M.A., Hasan, A.A.: A procedure for the positive definiteness of forms of even order. IEEE Transactions on Automatic Control 41(4), 615-617 (1996)
-
(1996)
IEEE Transactions on Automatic Control
, vol.41
, Issue.4
, pp. 615-617
-
-
Hasan, M.A.1
Hasan, A.A.2
-
19
-
-
0040962243
-
The discriminant of the characteristic polynomial of a normal matrix
-
[Ily92]
-
[Ily92] Ilyushechkin, N.V.: The discriminant of the characteristic polynomial of a normal matrix. Math. Zameski 51, 16-23 (1992)
-
(1992)
Math. Zameski
, vol.51
, pp. 16-23
-
-
Ilyushechkin, N.V.1
-
20
-
-
0040368135
-
-
; Englis translation in Math. Notes 51, 230-235 (1992)
-
(1992)
Math. Notes
, vol.51
, pp. 230-235
-
-
-
21
-
-
84968474102
-
Sharp effective nullstellensatz
-
[Kol88]
-
[Kol88] Kollár, J.: Sharp effective Nullstellensatz. J. Amer. Math. Soc. 1, 963-975 (1988)
-
(1988)
J. Amer. Math. Soc.
, vol.1
, pp. 963-975
-
-
Kollár, J.1
-
22
-
-
0035238864
-
Global optimization with polynomials and the problem of moments
-
[Las01]
-
[Las01] Lasserre, J.B.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796-817 (2001)
-
(2001)
SIAM J. Optim.
, vol.11
, Issue.3
, pp. 796-817
-
-
Lasserre, J.B.1
-
24
-
-
0032332990
-
On the discriminant of real symmetric matrices
-
[Lax98]
-
[Lax98] Lax, P.D.: On the discriminant of real symmetric matrices. Communications on Pure and Applied Mathematics LI, 1387-1396 (1998)
-
(1998)
Communications on Pure and Applied Mathematics
, vol.LI
, pp. 1387-1396
-
-
Lax, P.D.1
-
25
-
-
38149146720
-
Stable sets and polynomials
-
[Lov94]
-
[Lov94] Lovász, L.: Stable sets and polynomials. Discrete mathematics 124, 137-153 (1994)
-
(1994)
Discrete Mathematics
, vol.124
, pp. 137-153
-
-
Lovász, L.1
-
26
-
-
0001154274
-
Cones of matrices and set-functions and 0-1 optimization
-
[LS91]
-
[LS91] Lovász, L., Schrijver, A.: Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. 1(2), 166-190 (1991)
-
(1991)
SIAM J. Optim.
, vol.1
, Issue.2
, pp. 166-190
-
-
Lovász, L.1
Schrijver, A.2
-
28
-
-
0023452095
-
Some NP-complete problems in quadratic and nonlinear programming
-
[MK87]
-
[MK87] Murty, K.G., Kabadi, S.N.: Some NP-complete problems in quadratic and nonlinear programming. Mathematical Programming 39, 117-129 (1987)
-
(1987)
Mathematical Programming
, vol.39
, pp. 117-129
-
-
Murty, K.G.1
Kabadi, S.N.2
-
29
-
-
85036767048
-
The use of symbolic methods in control system analysis and design
-
[Mun99] Munro, N.: editor. IEE Books
-
[Mun99] Munro, N.: editor. The Use of Symbolic Methods in Control System Analysis and Design, volume 56 of Control engineering series. IEE Books, 1999
-
(1999)
Control Engineering Series
, vol.56
-
-
-
30
-
-
0001776805
-
Squared functional systems and optimization problems
-
[Nes00]. J.B.G. Frenk, C. Roos, T. Terlaky, S. Zhang, editors. Kluwer Academic Publishers
-
[Nes00] Nesterov, Y.: Squared functional systems and optimization problems. In: J.B.G. Frenk, C. Roos, T. Terlaky, S. Zhang, editors, High Performance Optimization, pages 405-440. Kluwer Academic Publishers, 2000
-
(2000)
High Performance Optimization
, pp. 405-440
-
-
Nesterov, Y.1
-
33
-
-
1542296013
-
An explicit construction of distinguished representations of polynomials nonnegative over finite sets
-
[Par02a]
-
[Par02a] Parrilo, P.A.: An explicit construction of distinguished representations of polynomials nonnegative over finite sets. Technical Report IfA Technical Report AUT02-02. Available from http://www.aut.ee.ethz.ch/ ~parrilo, ETH Zürich, 2002
-
(2002)
Technical Report IfA Technical Report
, vol.AUT02-02
-
-
Parrilo, P.A.1
-
36
-
-
0001276275
-
A new bound for Pólya's theorem with applications to polynomials positive on polyhedra
-
[PR01]
-
[PR01] Powers, V., Reznick, B.: A new bound for Pólya's theorem with applications to polynomials positive on polyhedra. J. Pure Appl. Algebra 164(1-2), 221-229 (2001)
-
(2001)
J. Pure Appl. Algebra
, vol.164
, Issue.1-2
, pp. 221-229
-
-
Powers, V.1
Reznick, B.2
-
38
-
-
0032064831
-
An algorithm for sums of squares of real polynomials
-
[PW98]
-
[PW98] Powers, V., Wörmann, T.: An algorithm for sums of squares of real polynomials. Journal of pure and applied algebra 127, 99-104 (1998)
-
(1998)
Journal of Pure and Applied Algebra
, vol.127
, pp. 99-104
-
-
Powers, V.1
Wörmann, T.2
-
39
-
-
0031674391
-
Copositive relaxation for general quadratic programming
-
[QDRT98]
-
[QDRT98] Quist, A.J., De Klerk, E., Roos, C., Terlaky, T.: Copositive relaxation for general quadratic programming. Optimization methods and software 9, 185-208 (1998)
-
(1998)
Optimization Methods and Software
, vol.9
, pp. 185-208
-
-
Quist, A.J.1
De Klerk, E.2
Roos, C.3
Terlaky, T.4
-
41
-
-
84972566433
-
Extremal PSD forms with few terms
-
[Rez78]
-
[Rez78] Reznick, B.: Extremal PSD forms with few terms. Duke Mathematical Journal 45(2), 363-374 (1978)
-
(1978)
Duke Mathematical Journal
, vol.45
, Issue.2
, pp. 363-374
-
-
Reznick, B.1
-
42
-
-
51249169659
-
Uniform denominators in Hilbert's seventeenth problem
-
[Rez95]
-
[Rez95] Reznick, B.: Uniform denominators in Hilbert's seventeenth problem. Math Z. 220, 75-97 (1995)
-
(1995)
Math Z.
, vol.220
, pp. 75-97
-
-
Reznick, B.1
-
43
-
-
0001157581
-
Some concrete aspects of Hilbert's 17th problem
-
[Rez00]. American Mathematical Society
-
[Rez00] Reznick, B.: Some concrete aspects of Hilbert's 17th problem. In: Contemporary Mathematics, volume 253, pages 251-272. American Mathematical Society, 2000
-
(2000)
Contemporary Mathematics
, vol.253
, pp. 251-272
-
-
Reznick, B.1
-
44
-
-
0001321687
-
A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
-
[SA90]
-
[SA90] Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Disc. Math. 3(3), 411-430 (1990)
-
(1990)
SIAM J. Disc. Math.
, vol.3
, Issue.3
, pp. 411-430
-
-
Sherali, H.D.1
Adams, W.P.2
-
46
-
-
0001250675
-
The k-moment problem for compact semialgebraic sets
-
[Sch91]
-
[Sch91] Schmüdgen, K.: The k-moment problem for compact semialgebraic sets. Math. Ann. 289, 203-206 (1991)
-
(1991)
Math. Ann.
, vol.289
, pp. 203-206
-
-
Schmüdgen, K.1
-
47
-
-
0000604097
-
Class of global minimum bounds of polynomial functions
-
[Sho87]
-
[Sho87] Shor, N.Z.: Class of global minimum bounds of polynomial functions. Cybernetics 23(6), 731-734 (1987);
-
(1987)
Cybernetics
, vol.23
, Issue.6
, pp. 731-734
-
-
Shor, N.Z.1
-
48
-
-
1842743052
-
-
Russian orig.: Kibernetika, 6, 9-11 (1987)
-
(1987)
Kibernetika
, vol.6
, pp. 9-11
-
-
-
50
-
-
34250416099
-
A nullstellensatz and a positivstellensatz in semialgebraic geometry
-
[Ste74]
-
[Ste74] Stengle, G.: A Nullstellensatz and a Positivstellensatz in semialgebraic geometry. Math. Ann. 207, 87-97(1974)
-
(1974)
Math. Ann.
, vol.207
, pp. 87-97
-
-
Stengle, G.1
-
51
-
-
0030162881
-
Complexity estimates for the schmüdgen positivstellensatz
-
[Ste96]
-
[Ste96] Stengle, G.: Complexity estimates for the Schmüdgen Positivstellensatz. J. Complexity 12(2), 167-174 (1996)
-
(1996)
J. Complexity
, vol.12
, Issue.2
, pp. 167-174
-
-
Stengle, G.1
-
52
-
-
0004943866
-
-
[Stu99] September
-
[Stu99] Sturm, J.: SeDuMi version 1.03. September 1999. Available from http://www.unim-aas.nl/~sturm/software/sedumi.html
-
(1999)
SeDuMi Version 1.03
-
-
Sturm, J.1
-
53
-
-
0002126665
-
Criteria for copositive matrices
-
[Väl86]
-
[Väl86] Väliaho, H.: Criteria for copositive matrices. Linear Algebra and its applications 81, 19-34 (1986)
-
(1986)
Linear Algebra and its Applications
, vol.81
, pp. 19-34
-
-
Väliaho, H.1
-
54
-
-
0030106462
-
Semidefinite programming
-
[VB96]
-
[VB96] Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review 38(1), 49-95 (1996)
-
(1996)
SIAM Review
, vol.38
, Issue.1
, pp. 49-95
-
-
Vandenberghe, L.1
Boyd, S.2
-
55
-
-
0003395487
-
-
[WSV00] Wolkowicz, H., Saigal, R., Vandenberghe, L.: editors. Kluwer
-
[WSV00] Wolkowicz, H., Saigal, R., Vandenberghe, L.: editors. Handbook of Semidefinite Programming. Kluwer, 2000
-
(2000)
Handbook of Semidefinite Programming
-
-
|