[英]Symbolic quadratic optimization with Maple
I'm trying to minimize a quadratic energy with linear equality constraints in Maple. 我正在尝试在Maple中使用线性相等约束最小化二次能量。 Currently I'm issuing things like: 目前,我正在发布以下内容:
with(Optimization):
p := (t) -> c3*t^3 + c2*t^2;
m := Minimize(int(diff(p(t),t)^2,t=0..1),{eval(p(t),t=1)=1,eval(diff(p(t),t),t=1)=0});
but this seems to give me a numerically optimized solution complete with floating point error: 但这似乎给了我一个数值优化的解决方案,并带有浮点误差:
m := [1.19999999999997, [c2 = 3.00000000000000, c3 = -2.00000000000000]]
(The correct answer is m:= [6/5,[c2=3,c3=-2]]) (正确答案是m:= [6/5,[c2 = 3,c3 = -2]])
Is there a way to compute the solution symbolically using maple? 有没有办法使用Maple 象征性地计算解决方案?
I'd rather not have to work out the Lagrangian myself. 我宁愿不必自己解决拉格朗日运动。 I'm hoping for a flag like symbolic=true. 我希望有一个像symbolic = true的标志。
Apply Lagrange multipliers step-by-step. 逐步应用拉格朗日乘数。 It's fairly easy to do. 这很容易做到。
p:= t-> c3*t^3+c2*t^2:
Obj:= int(D(p)^2, 0..1):
Con:= {p(1)=1, D(p)(1)=0}:
L:= Obj - l1*lhs(Con[1]) - l2*lhs(Con[2]):
solve(Con union {diff(L,c3), diff(L,c2)});
/ 12 -1\
{ c2 = 3, c3 = -2, l1 = --, l2 = -- }
\ 5 5 /
eval(Obj, %);
6
-
5
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