基础库中函数的一个示例是二次超线性函数quad_over_lin: (该函数也接受复数x,但我们将考虑实数x使事情变得简单。)二次超线性函数在x和y中是凸的,因此可以作为一个目标,适当的约束,或更复杂的表达 。 例如,我们可以使(Ax-b,cTx + d)的二次超线性函数最小化,使用 minimize( quad_over_lin( A* x - b...
quad_form(x,P) 对于实x和对称P, 对于复x和埃尔米特P, .当P固定和正半定,凸;当P固定和负半定,凹; 注意:二次函数(如quad_form,sum_square通常可以被norm函数替换,而不会牺牲等价性。出于数值原因,此替代公式是首选。有关详细信息,请参阅消除二次型。 quad_over_lin(x,y) 对于 , , ;对于 , , 。
quad_over_lin(x,y) \(x^Tx/y\)for\(x \in \mathbf{R}^n\),\(y >0\); for\(x \in \mathbf{C}^n\),\(y>0\),\(x^*x/y\). In CVX specification, adds constraint that\(y>0\). Outside CVX specification, returns\(+\infty\)if\(y\leq 0\). Convex, and decreasing in\(...
inv_pos,lambda_min,lambda_max,matrix_frac,quad_over_lin,sum_largest, and others. Some are a bit difficult to read because of diagnostic or error-checking code, but these are relatively simple.
minimize(quad_over_lin(A*x-b,c'*x+d)) 设置集合 CVX支持凸集的定义和使用,Matlab语言没有一个集合运算符,因此为了表示一个集合,我们使用一个返回一个未命名的变量的函数,该变量需要在集合中。我们用**==或In**来设定集合 //X被约束成等于一个未命名的变量,它必须是一个n×n对称正半定矩阵X==semidef...
Depending on the rest of the problem, the problem may or may not be convex, and maybe or maybe not it can be reformulated for CVX. Ifh_uBkis a quadratic, you can usequad_over_lin. Why isn't CVX accepting my model? READ THIS FIRST!FAQ ...
quad_over_lin(x,z)=1; 约束z=2*x-y;并不是⼀个等式约束,它是赋值操作。它将⼀个仿射表达式2*x-y的⽴即计算结果值存储下来,从⽽可以在后⾯的两个约束 中使⽤。我们将z称之为表达式持有符去和正式声明的CVX变量区分开来。 通常这对于将计算⼀组表达式的值放在⼀个MATLAB变量中是⼗分有...
quad_over_lin(x,y) x^Tx/yforx \in \mathbf{R}^n,y >0; forx \in \mathbf{C}^n,y>0,x^*x/y. In CVX specification, adds constraint thaty>0. Outside CVX specification, returns+\inftyify\leq 0. Convex, and decreasing iny. ...
1 cvx_begin和cvx_end 所有的cvx建模必须以cvx_begin开始以cvx_end结束，所有的变量声明，⽬标函数和约束必须位于这两者之 间，cvx_begin命令可以包含多个修饰词。cvx_begin quiet禁⽌求解过程中的屏幕输出 cvx_begin sdp调⽤半正定规划 cvx_begin gp调⽤⼏何规划 修饰词可以组合使⽤ 2变量 所有的变量...
quad_over_lin(affine, constant) matrix_frac(affine, constant) quad_form(affine, constant) Constructing and solving problems QCQPs must be represented using the standard CVXPY syntax. In order for the problem to be accepted byQCQP, the problem must have a quadratic objective function and quadratic...