| Abstrakt: |
Infeasible-interior-point paths $\{(x(r,\eta),y(r,\eta))\}_{r>0}$ , $0<\eta\in \mathbb{R}^n$ a positive vector, for a horizontal linear complementarity problem are defined as the solution of ( $q\in \mathbb{R}^n$ ) $$ \begin{array}{rclc} Px+Qy &=& q+r\bar q, & x>0, y>0, x_iy_i &=& r\eta_i, & 1\le i\le n. \end{array} \leqno(LCP)_r $$ If the path $z(r,\eta)=(x(r,\eta),y(r,\eta))$ converges for $r\downarrow 0$ , then it converges to a solution of $(LCP)_0$ . This paper deals with the analyticity properties of $z(r,\eta)$ and its derivatives with respect to r near r = 0 for solvable monotone complementarity problems $(LCP)_0$ . It is shown for $(LCP)_0$ with a strictly complementary solution that the path $z(r,\eta)$ , $r\downarrow0$ , has an extension to $r=0$ which is analytic also at $r=0$ . If $(LCP)_0$ has no strictly complementary solution, then $\hat z(\rho,\eta):=z(\rho^2,\eta)$ , $\rho=\sqrt r$ , has an extension to $\rho=0$ that is analytic at $\rho=0$ . [ABSTRACT FROM AUTHOR] |
Full text from SpringerLink