Cone Constructors
Constructor functions for the different cone types. Currently ROI supports eight different types of cones.
Zero cone
\mathcal{K}_{\mathrm{zero}} = \{0\}
Nonnegative (linear) cone
\mathcal{K}_{\mathrm{lin}} = \{x|x ≥q 0 \}
Second-order cone
\mathcal{K}_{\mathrm{soc}} = ≤ft\{(t, x) \ | \ ||x||_2 ≤q t, x \in R^n, t \in R \right\}
Positive semidefinite cone
\mathcal{K}_{\mathrm{psd}} = ≤ft\{ X \ | \ min(eig(X)) ≥q 0, \ X = X^T, \ X \in R^{n \times n} \right\}
Exponential cone
\mathcal{K}_{\mathrm{expp}} = ≤ft\{(x,y,z) \ | \ y e^{\frac{x}{y}} ≤q z, \ y > 0 \right\}
Dual exponential cone
\mathcal{K}_{\mathrm{expd}} = ≤ft\{(u,v,w) \ | \ -u e^{\frac{v}{u}} ≤q e w, u < 0 \right\}
Power cone
\mathcal{K}_{\mathrm{powp}} = ≤ft\{(x,y,z) \ | \ x^α * y^{(1-α)} ≥q |z|, \ x ≥q 0, \ y ≥q 0 \right\}
Dual power cone
\mathcal{K}_{\mathrm{powd}} = ≤ft\{ (u,v,w) \ | \ ≤ft(\frac{u}{α}\right)^α * ≤ft(\frac{v}{(1-α)}\right)^{(1-α)} ≥q |w|, \ u ≥q 0, \ v ≥q 0 \right\}
K_zero(size) K_lin(size) K_soc(sizes) K_psd(sizes) K_expp(size) K_expd(size) K_powp(alpha) K_powd(alpha)
size |
a integer giving the size of the cone,
if the dimension of the cones is fixed
(i.e. |
sizes |
a integer giving the sizes of the cones,
if the dimension of the cones is not fixed
(i.e. |
alpha |
a numeric vector giving the |
K_zero(3) ## 3 equality constraints K_lin(3) ## 3 constraints where the slack variable s lies in the linear cone
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