5.2 Modeling with the exponential cone 利用指数锥扩展圆锥优化工具箱,可以获得新类型的约束构件和新类型的可表示集合。本节将列出指数锥的基本操作。 5.2.1 Exponential 上镜图(epigraph)t≥ex是Kexp的一个部分: 5.2.2 Logarithm 同样,我们也可以表示下镜图t≤logx,x≥0: ...
The exponential cone is a convex subset of\(\R^3\)defined as (5.1)¶\[\begin{split}\begin{array}{rcl} \EXP & = & \left\{(x_1,x_2,x_3)~:~x_1\geq x_2 e^{x_3/x_2},\ x_2>0 \right\}\ \cup \\ & & \left\{(x_1,0,x_3)~:~x_1\geq 0,\ x_3\leq 0 \...
In this paper, we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a single univariate root-finding problem. This leads to a fast ...
We demonstrate the use and power of our results by computing tight error bounds for the exponential cone feasibility problem. Interestingly, we discover a natural example for which the tightest error bound is related to the Boltzmann-Shannon entropy. We were also able to produce an example of ...
functioncvx_optpnt=exponential(sx) %EXPONENTIALExponentialcone. %EXPONENTIAL,calledwithnoarguments,createsthreescalarvariablesX, %Y,andZandconstraintsthemtolieinanexponetialcone.Thatis, %giventhedeclaration %variablesxyz %{x,y,z}==exp_cone %constraintsthevariablestosatisfy ...
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1, Fig. 2 shows also an expansion of the rising thermal within the envelope given by a narrow cone, consistent with the observations. The maximum of the velocity is reached after about 10 minutes, corresponding to about three time scales, and the further evolution of the flow reduces this ...
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RegisterLog in Sign up with one click: Facebook Twitter Google Share on Facebook waveform (redirected fromtruncated exponential waveform) Thesaurus Medical Encyclopedia wave·form (wāv′fôrm′) n. The mathematical representation of a wave, especially a graph obtained by plotting a characteristic of...
The power singularities of solutions of the Dirichlet problem for strongly elliptic differential systems of order outside a slender cone are studied, where is a small positive parameter which characterizes the angle vertex of the cone... VG Mazya,SA Nazarov,BA Plamenevskiĭ - Mathematics of the...