Lines Matching refs:x_

29 f(x) = \sum_{i=0}^{m-1} \left( \alpha(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2 \right),
1629 ${x_1,x_2,\ldots,x_{N+1}}$ and their corresponding objective
1631 iteration, $x_{N+1}$ is removed from the set and replaced with
1634 x(\mu) = (1+\mu) \frac{1}{N} \sum_{i=1}^N x_i - \mu x_{N+1},
1882 contribution of $y_k \equiv \nabla f(x_k) - \nabla f(x_{k-1})$ in
2392 x_{k+1} = x_k - \alpha_k(J_k^T J_k)^{-1} J_k^T r(x_k)
2415   $\beta(x) = \frac{1}{2}||x_k - x_{k-1}||_2^2$
2462 point $x_+$ to be evaluated is obtained by solving the
2483 The residual vector is then evaluated to obtain $F(x_+)$ and hence
2484 $f(x_+)$. The ratio of actual decrease to predicted decrease,
2487 \rho_k = \frac{f(x_k)-f(x_+)}{m_k(x_k)-m_k(x_+)},
2494 x_{k+1} = \left\{\begin{array}{ll}
2495 x_+ & \text{if } \rho_k \geq \eta_1 \\
2496 x_+ & \text{if } 0<\rho_k <\eta_1  \text{ and \texttt{valid}=\texttt{true}}
2508 \eta_1 \text{ and } \|x_+-x_k\|_p\geq \omega_1\Delta_k \\
2521 algorithm tests whether the direction $x_+-x_k$ improves the