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2020
This chapter is devoted to the solution of saddle point problems that can be written in the abstract form $$\displaystyle \begin {cases} Au+B^{T}\lambda =F\\ Bu=G \end {cases} $$ for some linear operators A and B, λ having the role of a Lagrangian multiplier associated to the constraint Bu = G.
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This chapter is devoted to the solution of saddle point problems that can be written in the abstract form $$\displaystyle \begin {cases} Au+B^{T}\lambda =F\\ Bu=G \end {cases} $$ for some linear operators A and B, λ having the role of a Lagrangian multiplier associated to the constraint Bu = G.
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Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 1988
Abstract We have studied the ionization of rare gases by protons at intermediate energies, i.e., energies at which the velocities of the proton and the target-gas valence electrons are comparable. A significant channel for electron production in the forward direction is shown to be “saddle-point” ionization, in which electrons are stranded on or near
T.J. Gay +4 more
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Abstract We have studied the ionization of rare gases by protons at intermediate energies, i.e., energies at which the velocities of the proton and the target-gas valence electrons are comparable. A significant channel for electron production in the forward direction is shown to be “saddle-point” ionization, in which electrons are stranded on or near
T.J. Gay +4 more
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SADDLE POINTS OF PARABOLIC POLYNOMIALS [PDF]
Mathematics of the USSR-Sbornik, 1974 Let G(t, x) be the Green's function of a parabolic differential operator ∂/∂t + P(- i∂/∂x). In a previous article of the authors (Math. USSR Sb. 20 (1973), 519-542) estimates for G are obtained by means of a convex function νp invariantly defined by P, and the saddle points are distinguished under the assumption that νp is smooth.
M V Fedorjuk, S G Gindikin
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Conditional saddle-point configurations
Physical Review C, 1985A general method is presented for determining an equilibrium point on a potential energy surface subject to an arbitrary number of constraints. The method is then specialized to the calculation of a conditional saddle point in the liquid-drop model for which the constraint is the mass-asymmetry degree of freedom.
K. Thomas, Arnold J. Sierk, R. Davies
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On Convergence of the Arrow–Hurwicz Method for Saddle Point Problems
Journal of Mathematical Imaging and Vision, 2022B. He, Sheng Xu, Xiaoming Yuan
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International Journal of Game Theory, 1991
This paper considers three classes of matrices in terms of the existence ofsaddle points. The classes are described by conditions which are very closely related to the property ofquasi-concavity-convexity of functions of two variables. For the matrices in those classes, necessary and sufficient conditions for the existence of saddle points have been ...
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This paper considers three classes of matrices in terms of the existence ofsaddle points. The classes are described by conditions which are very closely related to the property ofquasi-concavity-convexity of functions of two variables. For the matrices in those classes, necessary and sufficient conditions for the existence of saddle points have been ...
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1991
The theorems in [7] dealing with classes 1A, 2A and 2B do not depend on the strategy sets being disjoint, and include all Silverman games where at least one player has an optimal pure strategy, except the symmetric 1 by 1 case: THEOREM 2.1. In the symmetric Silverman game (S,T,ν), suppose that there is an element c in S such that c < Tci for all ...
Gerald A. Heuer +1 more
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The theorems in [7] dealing with classes 1A, 2A and 2B do not depend on the strategy sets being disjoint, and include all Silverman games where at least one player has an optimal pure strategy, except the symmetric 1 by 1 case: THEOREM 2.1. In the symmetric Silverman game (S,T,ν), suppose that there is an element c in S such that c < Tci for all ...
Gerald A. Heuer +1 more
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Pseudo-duality and saddle points
Journal of Optimization Theory and Applications, 1981Results associated with saddle-type stationary points are described. It is shown that barrier-type functions are pseudo-duals of generalized Lagrangian functions, while augmented Lagrangians are pseudo-duals of the regular Lagrangian function. An application of pseudo-duality to a min-max problem is illustrated, together with several other examples.
Ury Passy, S. Yutav
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2010
The saddle point method is an asymptotic method to calculate integrals of the type $$ \int_{-\infty}^{\infty} e^{n\phi(x)} dx $$ (32.1) for large n. If the function o(x) has a maximum at x 0 , then the integrand also has a maximum there which becomes very sharp for large n.
Sighart F. Fischer +1 more
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The saddle point method is an asymptotic method to calculate integrals of the type $$ \int_{-\infty}^{\infty} e^{n\phi(x)} dx $$ (32.1) for large n. If the function o(x) has a maximum at x 0 , then the integrand also has a maximum there which becomes very sharp for large n.
Sighart F. Fischer +1 more
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1988
For reasonable shapes {α} described by a set of dimensionless deformation parameters the liquid drop deformation energy BDef exhibits a barrier for each value of the fissility x, cf. Eq. (1.75), for instance the configuration of two tangent spheres for x = 0 and a single sphere for x = 1. The deformation energy at the saddle deformation {\( \hat \alpha
William D. Myers, Rainer W. Hasse
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For reasonable shapes {α} described by a set of dimensionless deformation parameters the liquid drop deformation energy BDef exhibits a barrier for each value of the fissility x, cf. Eq. (1.75), for instance the configuration of two tangent spheres for x = 0 and a single sphere for x = 1. The deformation energy at the saddle deformation {\( \hat \alpha
William D. Myers, Rainer W. Hasse
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