Results 21 to 30 of about 585 (68)

Positivity of continuous piecewise polynomials

, 2011
Real algebraic geometry provides certificates for the positivity of polynomials on semi-algebraic sets by expressing them as a suitable combination of sums of squares and the defining inequalitites.
Plaumann, Daniel
core   +1 more source

Exploiting Group Symmetry in Truss Topology Optimization [PDF]

, 2007
AMS classification: 90C22, 20Cxx, 70 ...
Bai, Y.Q., de Klerk, E., Pasechnik, D.V., Sotirov, R.   +3 more
core   +2 more sources

Improving the linear relaxation of maximum k-cut with semidefinite-based constraints

EURO Journal on Computational Optimization, 2019
We consider the maximum k-cut problem that involves partitioning the vertex set of a graph into k subsets such that the sum of the weights of the edges joining vertices in different subsets is maximized.
VilmarJefté Rodrigues de Sousa, MiguelF. Anjos, Sébastien Le Digabel   +2 more
doaj  

LIBOR additive model calibration to swaptions markets [PDF]

, 2008
In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem.
Colino, Jesús P., Nogales, Francisco J., Stute, Winfried   +2 more
core   +1 more source

A bounded degree SOS hierarchy for polynomial optimization

EURO Journal on Computational Optimization, 2017
We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem (P):f∗=min{f(x):x∈K} on a compact basic semi-algebraic set K⊂Rn.
JeanB. Lasserre, Kim-Chuan Toh, Shouguang Yang   +2 more
doaj  

New approximations for the cone of copositive matrices and its dual

, 2012
We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for C
A Grundmann, E Klerk de, E Klerk de, EA Yildirim, IM Bomze, IM Bomze, IM Bomze, J Peña, J-B Hiriart-Urruty, JB Lasserre, Jean B. Lasserre, JW Gaddum, K Schmüdgen, KM Anstreicher, L Vandenberghe, M Schweighofer, RT Rockafellar   +16 more
core   +5 more sources

Block-diagonal semidefinite programming hierarchies for 0/1 programming [PDF]

, 2007
Lovasz and Schrijver, and later Lasserre, proposed hierarchies of semidefinite programming relaxations for general 0/1 linear programming problems. In this paper these two constructions are revisited and two new, block-diagonal hierarchies are proposed ...
Balas, Bollobás, Borchers, De Klerk, Frank Vallentin, Gvozdenović, Gvozdenović, Lasserre, Laurent, Laurent, Laurent, Lovász, Lovász, Monique Laurent, Nebojša Gvozdenović, Nemhauser, Schrijver, Sherali, Wolsey   +18 more
core   +4 more sources

Alternative SDP and SOCP approximations for polynomial optimization

EURO Journal on Computational Optimization, 2019
In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations for a general polynomial optimization problem (POP).
Xiaolong Kuang, Bissan Ghaddar, Joe Naoum-Sawaya, LuisF. Zuluaga   +3 more
doaj  

On the complexity of Putinar's Positivstellensatz [PDF]

, 2005
We prove an upper bound on the degree complexity of Putinar's Positivstellensatz. This bound is much worse than the one obtained previously for Schm\"udgen's Positivstellensatz but it depends on the same parameters.
Nie, Jiawang, Schweighofer, Markus
core   +6 more sources

A note on a matrix version of the Farkas lemma [PDF]

, 2012
A linear polyomial non-negative on the non-negativity domain of finitely many linear polynomials can be expressed as their non-negative linear combination.
Zalar, Aljaž
core   +1 more source