Lines Matching refs:_k

2172 \displaystyle \min_{u,v} & \tilde{f}_k(u, v) \\
2181 \tilde{f}_k(u,v) = f(u,v) - g(u,v)^T y^k + \frac{\rho_k}{2} \| g(u,v) \|^2
2217 \displaystyle \min_{\alpha \geq 0} \; \tilde{f}_k(u_k + \alpha du, v_k).
2249 \displaystyle \min_{u,v} & \tilde{f}_k(u, v) \\
2258 \displaystyle \min_{du,dv} & \tilde{f}_k(u_k+du, v_k+dv) \\
2273 \displaystyle \min_{dv} & \tilde{f}_k(u_k-A_k^{-1}(B_k dv + \alpha_k g_k), v_k+dv), \\
2281 \displaystyle \min_{dv} & \tilde{f}_k(u_{k+\frac{1}{2}} - A_k^{-1} B_k dv, v_{k+\frac{1}{2}}+dv). \\
2290 \displaystyle \min_{dv} & \frac{1}{2} dv^T \tilde{H}_k dv + \tilde{g}_{k+\frac{1}{2}}^T dv,
2294 where $\tilde{H}_k$ is the limited-memory quasi-Newton
2300 \tilde{g}_{k+\frac{1}{2}} & = & \nabla_v \tilde{f}_k(u_{k+\frac{1}{2}}, v_{k+\frac{1}{2}}) -
2301           \nabla_u \tilde{f}_k(u_{k+\frac{1}{2}}, v_{k+\frac{1}{2}}) A_k^{-1} B_k \\
2360 where $c_{k+1} = \nabla_u \tilde{f}_k (u_{k+1},v_{k+1})$ and
2361 $d_{k+1} = \nabla_v \tilde{f}_k (u_{k+1},v_{k+1})$. The