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A smooth vector field for quadratic programming
2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012In this paper we consider the class of convex optimization problems with affine inequality constraints and focus hereby on the class of quadratic programs. We propose a smooth vector field that is constructed such that its trajectories converge to the saddle point of the Lagrangian function associated to the convex optimization problem.
Christian Ebenbauer, Hans-Bernd Dürr
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On the global analysis of the planar quadratic vector fields
Nonlinear Analysis: Theory, Methods & Applications, 1997Using the concept of intersection multiplicity of projective curves, the author studies bifurcations of planar quadratic Hamiltonian systems (QHC). All bifurcation points (finite or infinite) of such systems are characterized by their intersection multiplicities.
Dana Schlomiuk
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A note on the completeness of homogeneous quadratic vector fields on the plane
Qualitative Theory of Dynamical Systems, 2005The authors give a full description of the complete homogeneous quadratic vector fields defined on the plane. The main results obtained are as follows. Main results: Let \(F\) be a homogeneous quadratic vector field defined on the plane. Then the following assertions are equivalent: (1) \(F\) is complete; (2) \(F\) is quadratic-affine or the equation \(
Alberto Medina
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Vector fields and quadratic maps
The Journal of the Acoustical Society of America, 1998Vector fields describing responses of nonlinear systems are often investigated by sampling on a suitable Poincaré section. For example, period-1 limit cycles yield one fixed point, period-2 two points, and so on. More information could be obtained if the full return map on the section rather than just the fixed points were known.
Huw G. Davies, Konstantinos Karagiosis
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Quadratic vector fields in class I
Dynamical SystemsIn [Ye et al., Theory of Limit Cycles, 1986], quadratic systems are classified into three different normal forms (I, II and III) with increasing number of parameters. The simplest family is I and even several subfamilies of it have been studied, and some global attempts have been done, up to this paper, the full study was still undone. In this article,
Artés Ferragud, Joan Carles +3 more
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A Summary of Structurally Stable Quadratic Vector Fields
2018To make this work self-contained, we are going to summarize in this chapter all the needed results from the paper of Artes et al. (Mem. Am. Math. Soc. 134(639), 1998). For the results of the present paper, the realizable structurally stable quadratic vector fields and the non-realizable ones are very important.
Joan C. Artés +2 more
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