Summary of Tao Solvers — PETSc 3.25.1 documentation

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# Summary of Tao Solvers

## Unconstrained

Algorithm | Associated Type | Objective | Gradient | Hessian | Constraints | Jacobian
--- | --- | --- | --- | --- | --- | ---
Nelder-Mead | `TAONM` | X |  |  |  |
Conjugate Gradient | `TAOCG` | X | X |  |  |
Limited Memory Variable Metric (quasi-Newton) | `TAOLMVM` | X | X |  |  |
Orthant-wise Limited Memory (quasi-Newton) | `TAOOWLQN` | X | X |  |  |
Bundle Method for Regularized Risk Minimization | `TAOBMRM` | X | X |  |  |
Newton Line Search | `TAONLS` | X | X | X |  |
Newton Trust Region | `TAONTR` | X | X | X |  |

## Bound Constrained

Algorithm | Associated Type | Objective | Gradient | Hessian | Constraints | Jacobian | Constraint Type
--- | --- | --- | --- | --- | --- | --- | ---
Bounded Conjugate Gradient | `TAOBNCG` | X | X |  |  |  | Box constraints
Bounded Limited Memory Variable Metric (Quasi-Newton) | `TAOBLMVM` | X | X |  |  |  | Box constraints
Bounded Quasi-Newton Line Search | `TAOBQNLS` | X | X |  |  |  | Box constraints
Bounded Newton Line Search | `TAOBNLS` | X | X |  |  |  | Box constraints
Bounded Newton Trust-Region | `TAOBNTR` | X | X |  |  |  | Box constraints
Gradient Projection Conjugate Gradient | `TAOGPCG` | X | X |  |  |  | Box constraints
Bounded Quadratic Interior Point | `TAOBQPIP` | X | X |  |  |  | Box constraints
Tron | `TAOTRON` | X | X | X |  |  | Box constraints

## Complementarity

Algorithm | Associated Type | Objective | Gradient | Hessian | Constraints | Jacobian | Constraint Type
--- | --- | --- | --- | --- | --- | --- | ---
Active-Set Feasible Line Search | `TAOASFLS` |  |  |  | X | X | Complementarity
Active-Set Infeasible Line Search | `TAOASILS` |  |  |  | X | X | Complementarity
Semismooth Feasible Line Search | `TAOSSFLS` |  |  |  | X | X | Complementarity
Semismooth Infeasible Line Searchx | `TAOSSILS` |  |  |  | X | X | Complementarity

## Nonlinear Least Squares

Algorithm | Associated Type | Objective | Gradient | Hessian | Constraints | Jacobian | Constraint Type
--- | --- | --- | --- | --- | --- | --- | ---
POUNDERS | `TAOPOUNDERS` | X |  |  |  |  | Box Constraints

## PDE-Constrained

Algorithm | Associated Type | Objective | Gradient | Hessian | Constraints | Jacobian | Constraint Type
--- | --- | --- | --- | --- | --- | --- | ---
Linearly Constrained Lagrangian | `TAOLCL` | X | X | X | X | X | PDE Constraints

## Constrained

Algorithm | Associated Type | Objective | Gradient | Hessian | Constraints | Jacobian | Constraint Type
--- | --- | --- | --- | --- | --- | --- | ---
Interior Point Method | `TAOIPM` | X | X | X | X | X | General Constraints
Barrier-Based Primal-Dual Interior Point | `TAOPDIPM` | X | X | X | X | X | General Constraints