1.norm(x,n):x的n范数，在SOCP中经常使用
2.当对QP问题优化时，最好引入辅助变量，这使得内点算法面临的矩阵稀疏化，有利于快速求解
aux = sdpvar(length(residuals),1);
solvesdp([aux == residuals],aux'*aux);
3.方阵默认是对称的，因此>=0是正定的意思；非方阵以及full paremeterized方阵（如P = sdpvar(3,3,'full')）>=0是针对每个元素而言的
4.所有约束用一个[]扩起来，“,”号分割
  C = [P>=0, P(1,1)<=2, sum(sum(P))==10];
5.几种特殊矩阵（也可以用sdpvar()的第三个参数来指定）
x = sdpvar(n,1);
D = diag(x) ;    % Diagonal matrix
H = hankel(x);   % Hankel matrix
T = toeplitz(x); % Toeplitz matrix
6.SOCP的建模与求解
Let us continue with our regression problem from the linear and quadratic programming tutorial.

The problem boiled down to solving the problem minimize ||Ax-y|| for some suitable norm. Let us select the 2-norm, but this

time solve the extension where we minimize the worst-case cost, under the assumption that the matrix A is uncertain,A=A+d,

where ||d||2<1. This can be shown to be equivalent to minimizing ||Ax-y||2 + ||x||2.

This problem can easily be solved using YALMIP. Begin by defining the data.
x = [1 2 3 4 5 6]';
t = (0:0.02:2*pi)';
A = [sin(t) sin(2*t) sin(3*t) sin(4*t) sin(5*t) sin(6*t)];
e = (-4+8*rand(length(A),1));
y = A*x+e;


As a first approach, we will do the modelling by hand, by adding second order cones using the low-level command cone.
xhat = sdpvar(6,1);
sdpvar u v

F = [cone(y-A*xhat,u), cone(xhat,v)];
solvesdp(F,u + v);


By using the automatic modelling support in the nonlinear operator framework, we can alternatively write
solvesdp([],norm(y-A*xhat,2) + norm(xhat,2));

YALMIP will automatically model this as a second order cone problem, and solve it as such if a second order cone programming

solver is installed (SeDuMi, SDPT3 or Mosek). If no second order cone programming solver is found, YALMIP will convert the

model to a semidefinite program and solve it using any installed semidefinite programming solver.