Lines Matching refs:where
32 where $n = 2m$ is the number of variables. Note that while we use
252 that identifies where the objective should be evaluated, and the fourth
282 where the first argument is the TAO solver object, the second argument
311 where the first argument is the TAO solver and the second argument
322 where the arguments are the TAO application, the optional vector to be
343 where the first argument of this routine is a TAO solver object. The
361 third arguments are, respectively, the Mat object where the Hessian will
432 the appropriate TAO interface functions and call-back routines where necessary.
486 where the first and last arguments are the TAO solver object and the application
548 where $X$ is the current approximation to the true solution
634 where the state variable $u$ is the solution to the discretized
646 Unlike other TAO solvers where the solution vector contains only the
656 where the first IS is a PETSc IndexSet containing the indices of the
660 where $c: \mathbb R^n \to \mathbb R^m$. These constraints should
774 nonlinear equations $C(X) = 0$, where
894 to obtain a step $d_k$, where $H_k$ is the Hessian of the
896 objective function at $x_k$. For problems where the Hessian matrix
903 is solved to obtain the direction, where $\rho_k$ is a positive
1143 where $g(x_k)$ is the gradient of the objective function and
1162 where $g(x_k)$ is the gradient of the objective function and
1176 where $g(x_k)$ is the gradient of the objective function,
1180 $\rho_{k+1} < \text{pmin}$, then $\rho_{k+1} = 0$, where
1205 line argument, where the default value is 100. The `direction`
1226 where
1233 where $q_k$ is the quadratic model. The radius is then updated as
1246 where
1268 to obtain a direction $d_k$, where $H_k$ is the Hessian of
1480 line argument, where the default value is 100. The `direction`
1491 where $q_k$ is the quadratic model. The radius is then updated as
1504 where
1538 where $H_k$ is the Hessian approximation obtained by using the
1573 In applications where `TaoSolve()` on the LMVM algorithm is repeatedly
1637 where $\mu$ can be one of
1739 $w_k = x_k - \mathfrak{B}(x_k - \beta D_k g_k)$, where the
1775 problems where the Hessian evaluation is disproportionately more
1791 where $\rho_k$ is a dynamically adjusted positive constant. The
1805 machine epsilon, scaled by the latest function value, where the full
1884 is equal to $1.0$ by default. There are also times where we want
1919 function in the code is `TaoBNCGSetH0(tao, H0)` where `H0` is the
1939 $Mn$ iterations, where $n$ is the problem dimension and
1970 where $x \in \mathbb R^n$, $z \in \mathbb R^m$,
2013 certain cases where augmented Lagrangian’s Hessian may become nearly
2031 where $g(x)$ are equality constraints, $h(x)$ are inequality
2046 where $L(x, \lambda_k)$ is the augmented Lagrangian merit function
2111 where, $\lambda_{ce}$ and $\lambda_{ci}$ are the Lagrangian
2150 where the state variable $u$ is the solution to the discretized
2177 where $A_k = \nabla_u g(u_k,v_k)$,
2294 where $\tilde{H}_k$ is the limited-memory quasi-Newton
2360 where $c_{k+1} = \nabla_u \tilde{f}_k (u_{k+1},v_{k+1})$ and
2395 where $r(x)$ is the least-squares residual vector,
2410 where $\lambda$ is the scalar weight of the regularizer. BRGN
2418 where $y = Dx$ and $\epsilon$ is the smooth approximation
2431 `-tao_brgn_regularization_type <l2pure, l2prox, l1dict, user>` where the `user` option allows
2472 where $\Delta_k$ is the current trust-region radius. By default we
2516 where $0 < \eta_1 < 1$, $0 < \gamma_0 < 1 < \gamma_1$,
2523 $F(x_k+d_k)$, where $d_k$ is a model-improving direction.
2656 MCP($\nabla f$, $\ell$, $u$), where
2703 of equations $\Phi(x) = 0$, where
2728 $H^kd^k = -\Phi(x^k)$, where $H^k$ is an element of the
2759 where the direction in this case corresponds to the first part of the
2802 where the gradient and the Hessian of the objective are both constant.
3399 where `name` is the name of the solver (i.e., `tao_blmvm`), `path`