from IPython.display import Image
fig=Image(url='http://mathopt.sakura.ne.jp/LP1.png')
fig

import picos as pic
P=pic.Problem()
x=P.add_variable('x',2)
P.add_constraint(x[0]>x[1])
P.add_constraint(x[0]<=3)
P.add_constraint(x[0]+x[1]<=4)
objective=0.5*x[0]+x[1]
P.set_objective('max',objective)
print P
P.solve(solver='cvxopt',verbose=False);
print P.obj_value()



fig2=Image(url='http://mathopt.sakura.ne.jp/LP2.png')
fig2

import cvxopt as cvx
A=pic.new_param('A',cvx.matrix([[-1,1,1],[1,0,1]]))
b=[0,3,4]
c=[0.5,1]

P=pic.Problem()
x=P.add_variable('x',2)
objective=(c|x)
P.set_objective('max',objective)
P.add_constraint(A*x<=b)
print P
P.solve(solver='cvxopt',verbose=False);
print P.obj_value()

SDP1=Image(url='http://mathopt.sakura.ne.jp/SDP1.png')
SDP1

SDP2=Image(url='http://mathopt.sakura.ne.jp/SDP2.png')
SDP2

SDP3=Image(url='http://mathopt.sakura.ne.jp/SDP3.png')
SDP3

SDP4=Image(url='http://mathopt.sakura.ne.jp/SDP4.png')
SDP4

SDP5=Image(url='http://mathopt.sakura.ne.jp/SDP5.png')
SDP5

A={}
A[0]=pic.new_param('A0',cvx.matrix([[0,0,0],[0,3,0],[0,0,4]]))
A[1]=pic.new_param('A1',cvx.matrix([[-1,0,0],[0,1,0],[0,0,1]]))
A[2]=pic.new_param('A2',cvx.matrix([[1,0,0],[0,0,0],[0,0,1]]))
b=[0.5,1.0]

sdp=pic.Problem()
z=sdp.add_variable('z',2)
objective=(b|z)
sdp.set_objective('max',objective)
sdp.add_constraint(A[0]-z[0]*A[1]-z[1]*A[2]>>0)
print sdp

sdp.solve(solver='cvxopt',verbose=False);
print sdp.obj_value()

SOCP1=Image(url='http://mathopt.sakura.ne.jp/SOCP1.png')
SOCP1

import math
import random
a={}
a[0]=[random.randint(1,5)*10 for i in range(1,4)]
a[1]=[random.randint(1,5)*10 for i in range(1,4)]
a[2]=[random.randint(1,5)*10 for i in range(1,4)]
b=[0.5,1]


socp=pic.Problem()
z=socp.add_variable('z',2)
objective=(b|z)
socp.set_objective('max',objective)
socp.add_constraint(abs((a[0]-z[0]*a[1]-z[1]*a[2])[1:] )< (a[0]-z[0]*a[1]-z[1]*a[2])[0])
print socp

socp.solve(solver='cvxopt');
print socp.obj_value()