r****o
发帖数: 1950 | 1 看到convex optimization的一个结论是
convex set上的convex函数的local minimum即为global minimum
convex set上的concave函数的local maximum即为global maximum
请问这个global minum或global maximum是否考虑了边界点的情况。
例如f(x) concave，定义域为[a,b]，假如f(x)在(a,b)上存在local maximum，
那么这个local maximum是(a,b)上的global maximum呢，还是[a,b]上的global
maximum呢？
多谢指教。 |
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b***k
发帖数: 2673 | 2 ☆─────────────────────────────────────☆
NPC (npc) 于 (Wed Jul 2 13:50:24 2008) 提到:
I come across a problem like this the other day:
Long a FRA short a EuroDollar, the dates are the same,Is the convexity
positive or negative?
I think I have some conceptual confusion. How does one calculate the
convexity of such a portfolio?In what sense does this convexity here mean?
usually
y=y_0+(convexity term)
what is puzzling for me is what is the y and y_0 in this case?One may say
r_fwd=r_fut-0.5sigma^ |
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w****h
发帖数: 212 | 3 【 以下文字转载自 Mathematics 讨论区 】
发信人: wmbyhh (wmbyhh), 信区: Mathematics
标 题: 问一个关于convex set的数学问题
发信站: BBS 未名空间站 (Thu Apr 3 16:06:18 2008)
假如Y是个离散随机变量,其概率分布为P(Y=a_{i})=x_{i}, i=1, 2...n,
已知a_{1}
现在我需要证明x=k*x_{i}+(1-k)*x_{j}也在这个X里，才能知道X是否是convex set.
但是，E(Y^2)=\sum [(a_{i})^2*x_{i}]<=c,x是一个概率，对应一个数a_{x},如何证明x也满足这个条
件呢？ |
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c*******s
发帖数: 179 | 4 sorry for only typing English.
Please help me to clarify the attached figure, in which the protrusion 1
is a convex shape, and protrusion 2 and 3 are two concave shapes?
what I think is that 1 is convex with k_1>k_2>0, while 2 and 3 are concave
with k_1
if the orientation of the whole surface is consistently defined (this is his
conclusion).
which one is more conviced? |
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s********l
发帖数: 4 | 5 E_y(f(x;y)) of a function f(x;y), convex in x for each y,
how can I go one step further to show that over the
R.V. y is convex.Is this joitly convex in x and y or separately? thanks a
lot!!!! |
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s********l
发帖数: 4 | 6 f(x,y) is convex in x for each y (fixing y first), I want to show that f(x,y) is also convex over y.further I wanna know whether this is jointly convex or separately. Thanks again |
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c*******v
发帖数: 2599 | 7 y从0到pi/2
(sin y) x^2 对每个固定的y是凸的。
但是固定x,就对y不凸。
E_y(f(x;y)) of a function f(x;y), convex in x for each y,
how can I go one step further to show that over the
R.V. y is convex.Is this joitly convex in x and y or separately? thanks a
lot!!!! |
|
A*******r
发帖数: 768 | 8 这样吧，
你把
Fundamentals of Convex Analysis (Grundlehren Text Editions)
Jean-Baptiste Hiriart-Urruty, Claude Lemarechal
看一遍吧
这个是精简本，实在不行就看那个两卷本的
那个
Convex Analysis
by Ralph Tyrell Rockafellar
也可以看看
这个是气宗的练法
资质好的三年有成，资质一般的五年七年吧
剑宗的练法简单一点
Convex Analysis and Optimization
by Dimitri Bertsekas
Boyd 的那本
Vandenberghe 的关于 semidefinite programming 的书
Luenberg的那本书
Chatal + Dantzig的书
Horn and Johnson的矩阵轮
Wright + Ye的内点法的书
bla bla bla
看你具体做什么哈
一年有成 |
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a********e
发帖数: 508 | 9 问题没提得很具体，我就假设是hedge negative convex的market downside risk
OMT put option正好downside payout是postive convex
具体到不同的asset class，都能用类似的option hedge
不过问题还是说清楚什么东西的negative convex risk才能有更清楚的答案 |
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P*****f
发帖数: 2272 | 10 【 以下文字转载自 Mathematics 讨论区 】
发信人: Pontiff (diablo), 信区: Mathematics
标 题: 这个函数是convex的麻?
发信站: BBS 未名空间站 (Wed Sep 14 23:47:27 2005), 转信
如果f(x)在[a,b] differentiable, 且其 first order derevative g(x) 在
[a.b]连续并且单调递增.
f(x)是convex得马？
反正俺画出来的几何图形的确是一段向下凸的curve.
thx |
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f**********g
发帖数: 107 | 11 这个什么定理都不用。取决于你所说的convex set指的是 (a,b)还是[a,b]。如果(a,b)
是convex set，那么local optimum在(a,b)上就是global。 |
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w****h
发帖数: 212 | 12 假如Y是个离散随机变量,其概率分布为P(Y=a_{i})=x_{i}, i=1, 2...n,
已知a_{1}
现在我需要证明x=k*x_{i}+(1-k)*x_{j}也在这个X里，才能知道X是否是convex set.
但是，E(Y^2)=\sum [(a_{i})^2*x_{i}]<=c,x是一个概率，对应一个数a_{x},如何证明x也满足这个条
件呢？ |
|
|
d*j
发帖数: 13780 | 14 一般桌子上，就是输入curve 得到一个点， 然后curev +/- 5 , +/-10 等等
不同点上得到不同的值
画条曲线看看
开口朝上就是 positive convex 朝下 相反
直线就是没有 convex |
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x**8
发帖数: 1939 | 15 我试图理解一下，大侠看看对不对，
callable bond 有 negative convexity,
put option 可以 hedge call option, 所以puttable bond 即可以hedge negative
convexity,
是这样么？
才反应过来，当时就蒙菜了，唉 |
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A****F
发帖数: 1133 | 16 我的想法很简单 就是putable bond的convexity is always positive 所以可以对冲
negative convexity |
|
发帖数: 1 | 17 凡是有optionality的产品都可以啊
put-call parity告诉我们对于gamma来说，call和put都一样，所以选择哪个来hedge都
一样
具体来讲，对于利率，callable bond/putable bond都可以，你只需要选择long或者
short就可以了，long positive convexity product = short negative convexity
product |
|
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r*****k
发帖数: 1281 | 19 【 以下文字转载自 EE 讨论区 】
发信人: rethink (considering), 信区: EE
标 题: convex programming有啥好的solver吗？
发信站: BBS 未名空间站 (Wed Feb 10 21:55:54 2010, 美东)
几百个变量
几百个constraint
用过的请推荐下，3x！ |
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t****t
发帖数: 6806 | 20 你理解有误吧?
我的理解是这样
x_i = k*x1_i+(1-k)x2_i
if x1\in X, x2\in X, then x\in X
就是说, X是the set of all possible *set* of x_i 's that satisfy ....
the condition E(Y^2)<=c,现在该如何证明X是个convex set?
明x也满足这个条 |
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w****h
发帖数: 212 | 21 好吧，我确实觉得单个x无法满足。
但是，按你说的，现在如何证明X是convex set呢？
如何证明k*x1_{i}+(1-k)*x2_{i}也满足E(Y^2)<=c |
|
k****f
发帖数: 3794 | 22 x_i > 0
\sum a_i^2 x_i <= c
这些约束对x_i来说，都是线性的
线性的半平面是凸集，他们的交集，自然是凸集的。
the condition E(Y^2)<=c,现在该如何证明X是个convex set?
明x也满足这个条 |
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o*********y
发帖数: 65 | 23 Suppose we have a function F(X) that we can evaluate. X is a vector, and
suppose F() is convex. In this case, what is the best strategy (minimal steps
to find minimal) to find the minimal?
My current naive idea needs 2^n+n+1 times evaluation each step (n is the
dimention of X). I guess this should be a classic problem, I wonder what's
the best strategies known? thanks a lot, bow. |
|
h***o
发帖数: 26 | 24 convex surface, only one minima
newton method should be most effiecient |
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h********e
发帖数: 4 | 25 Can anybody tell me a fast and robust algorithm to determine whether a
vector point x is inside a cone formed by a set of vector points {x1, x2, ..
., xn}? x1, x2, ..., xn can be linear dependent. Cone is the linear
summation of {x1, x2, ..., xn} with non-negative coefficients.
A similar question is how to determine whether x is inside the convex hull
formed by {x1, x2, ..., xn}.
Thank you. |
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b****t
发帖数: 29 | 26 谁能举个关于convex的函数但是不是连续的？ |
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n*******l
发帖数: 2911 | 27 Teman and Ekeland, Convex analysis and variational problems. |
|
p*******s
发帖数: 7 | 28 一般来说这个log likelihood function 是几个loggamma函数的代数和。有没有一般方法
知道其convexity? |
|
h********e
发帖数: 4 | 29 Can anybody tell me a fast and robust algorithm to determine whether a
vector point x is inside a cone formed by a set of vector points {x1, x2, ..
., xn}? x1, x2, ..., xn can be linear dependent. Cone is the linear
summation of {x1, x2, ..., xn} with non-negative coefficients.
A similar question is how to determine whether x is inside the convex hull
formed by {x1, x2, ..., xn}.
Thank you. |
|
r*****f
发帖数: 247 | 30 tr{(S'AS+B)^(-1)}
S，A，B都是矩阵，其中S是未知的变量，A和B都是正定的矩阵。
S'是S的hermitian。
请问这个方程关于S是convex的么？ |
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r****o
发帖数: 1950 | 31 如果[a,b]是convex set，那么local optimum在[a,b]上还是global吗？
b) |
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w****h
发帖数: 212 | 32 是我没讲清楚吗？
已知a_{1}
Y^2)<=c,现在该如何证明X是个convex set. |
|
t****t
发帖数: 6806 | 33 check my answer in programming...
the condition E(Y^2)<=c,现在该如何证明X是个convex set?
明x也满足这个条 |
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b***k
发帖数: 2673 | 34 ☆─────────────────────────────────────☆
jeannie (Nokia) 于 (Sun Jun 8 23:26:00 2008) 提到:
谢谢
☆─────────────────────────────────────☆
echostate (AI) 于 (Mon Jun 9 00:42:04 2008) 提到:
Convex Optimization by Stephen Boyd and Lieven Vandenberghe
Definitely the first choice.
BTW,
You can find the free e-book, excellent slides, some exercise, and very
useful software in the author's website at http://www.stanford.edu/~boyd/cvxbook/
☆─────────────────────────────────────☆
jeannie (Nokia) 于 |
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l*****i
发帖数: 3929 | 35 use definition of "convexity" itself |
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A**u
发帖数: 2458 | 36 这就是convex 定义
与下面的关系等价， X1 < X2 < X3
(C(X2)-C(X1))/(X2-X1) < (C(X3)-C(X2))/(X3-X2);
这两个关系 用中值定理证明， 充分必要
第二关系(x1,x2)的slope 小于 (x2,x3)的slope 是option的3个性质之一 |
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d**t
发帖数: 183 | 37 I think we need to prove c is a convex function of s instead of k.
construct a butterfly: long 1 call at k-e, long 1 call at k e, short 2 calls
at k,the va........
★ Sent from iPhone App: iReader Mitbbs Lite 7.28 |
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k*****y
发帖数: 744 | 38 到底是问关于spot price还是关于strike是convex的？ |
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t******L
发帖数: 5 | 39 比如我short一个ED，那这个convexity是正的还是负的，为什么？ |
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d*j
发帖数: 13780 | 40 我还一直以为是零那。。。。 不过和dv01比起来这个二阶的确实小太多了。。。。
long ED convexity 是正的 |
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t******L
发帖数: 5 | 41 both.. if long a FRA and short ED?
I have an impression that FRA doesn't really have convexity???
I dont really understand that's why I ask... |
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Y******u
发帖数: 1912 | 42 额。。。ED Convex难道不是0么，price不是100 - yield么,dv01不是固定的0.25? |
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L*****k
发帖数: 327 | 43 co-ask, eurodollor的convexity是0吧 |
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b********e
发帖数: 74 | 44
Eurodollar future is mark to market daily. If you are long ED, when rate
goes up, you lose money so need to post margin. When rate falls, you get
credit in your account but unfortunately your return for the credit
reinvestment is lower since we are in lower rate environment. We pay when
rate goes up and we get back when rate goes down. So in some sense there is
negative convexity. ED investor will be compensated by letting future rates
to be above corresponding forward rate (from FRA). This is ... 阅读全帖 |
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n*******l
发帖数: 2911 | 45
Let {Vi}, i=1:n be n vectors.
a1*V1 + a2*V2 +...+an*Vn
is a convex linear combination of {Vi} if
all ai>= 0 and a1+a2+...+an = 1. |
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|
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j******l
发帖数: 1068 | 48 Discrete Convex 同传统的Continuous Convex 的关系就有点象 Integer Programming
同 Linear Programming的关系。
Continuous Convex的理论70年代就基本成熟了。最经典的是70年的Rockafellar的
Convex Analysis。我就是读该书入门的。日本的几个数理工学家最近10年就在把
Continuous Convex的东西全部离散化（Discrete），例如最基本的continuous convex
Function 被他们用两个离散函数来表达（L-convex function, M-convex function）。
我们实际问题的大多数variable都是离散型的。所以他们的这项工作是很有意义的。
Discrete Convex 现在刚刚开始被日本及几个美国（Duke的Zipkin，Song）的研究者应
用到经济，经营，Game Theory，概率论里面。 |
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c***z
发帖数: 6348 | 49 节选自http://michaelochurch.wordpress.com/2013/04/03/gervais-macleod-21-why-does-work-suck/
[Companies] have several phases, each deserving its own moral stance:
Financial risk transfer. Entrepreneurs put capital and their reputations at
risk to amass the resources necessary to start a project whose returns are (
macroscopically, at least) convex. This pool of resources is used to pay
bills and wages, therefore allowing workers to get a reliable, recurring
monthly wage that is somewhat less than th... 阅读全帖 |
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n*********3
发帖数: 534 | 50 板子 cost money, you can just use a carboard. It all depends on your long
term goal/desire.
"大人也适合长期玩的" there are many options, and price range. It again
depends on your long term goal/desire, and preference.
Do you like double convex (japanese and korean style) or single convex (
chinese style)? I personally only like single convex.
For chinese style, the popular and quite well accepted standard is YunZi,
but they are really just one type of glass and great art work for yesterday
or many decades ... 阅读全帖 |
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