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

Summary of Nonlinear Solvers Available In PETSc Downloading PETSc