Some properties of K-convex mappings in variable ordering settings

Figures & data

Figure 1. A cone of separations for $x^1,x^2\in {\mathbb{R}}^n$ when m = 2.

Table

$y_1$	$y_2$	$v_1^1\left(y\right)$	$v_2^1\left(y\right)$	$v_1^2\left(y\right)$	$v_2^2\left(y\right)$
0	0	$0.71$	$-0.71$	$0.71$	$0.71$
$0.5$	0	$0.71$	$-0.71$	$0.44$	$0.89$
1	1	$0.32$	$-0.95$	$0.32$	$0.95$

Figure 2. A minimal variable K-convexification for m = 2. (a) $y=(0,0{)}^T$, (b) $y=(0.5,0{)}^T$ and (c) $y=(1,1{)}^T$.

Figure 3. Application of Theorem 5.1 for $F\left(t\right)=(t^2,t^3{)}^T$ with $\alpha =-1$ and $\text{β}=1$. (a) $t_0=-1$, (b) $t_0=0.15$ and (c) $t_0=1$.