Reference

Base type for an optimization model with degenerate constraints.

min f(x)
l <= x <= u
lb <= c(x) <= ub
0 <= G(x) _|_ H(x) >= 0

MPCCCounters

Initialization: MPCCCounters()

A composite type that represents the main features of the optimization problem

optimize obj(x) subject to lvar ≤ x ≤ uvar lcon ≤ cons(x) ≤ ucon lcc ≤ G(x) | H(x) >= ucc

where x is an nvar-dimensional vector, obj is the real-valued objective function, cons is the vector-valued constraint function, optimize is either "minimize" or "maximize".

Here, lvar, uvar, lcon and ucon are vectors. Some of their components may be infinite to indicate that the corresponding bound or general constraint is not present.

Convert an MPCCModel to an NLPModels as follows. Definit le type NLMPCC : min f(x) s.t. l <= x <= u lcon(tb) <= cnl(x) <= ucon

with

cnl(x) := c(x),G(x),H(x),G(x).*H(x)

reset!(nlp)

Reset evaluation count in nlp

reset!(counters)

Reset evaluation counters

complementarity_constrained(nlp)
complementarity_constrained(meta)

Returns whether the problem's constraints are all inequalities. Unconstrained problems return true.

c = consG(nlp, x, c)

Evaluate the constraints of consG at x in place.

Evaluate $G(x)$, the constraints at x.

c = consG(nlp, x, c)

Evaluate the constraints of consG at x.

c = consG_lin!(nlp, x, c)

Evaluate the linear constraints at x in place.

c = consG_lin(nlp, x, c)

Evaluate the linear constraints at x.

c = consG_nln!(nlp, x, c)

Evaluate the nonlinear constraints at x in place.

c = consG_nln(nlp, x, c)

Evaluate the nonlinear constraints at x.

c = consH(nlp, x, c)

Evaluate the constraints of consH at x in place.

Evaluate $H(x)$, the constraints at x.

c = consH(nlp, x, c)

Evaluate the constraints of consH at x.

c = consH_lin!(nlp, x, c)

Evaluate the linear constraints at x in place.

c = consH_lin(nlp, x, c)

Evaluate the linear constraints at x.

c = consH_nln!(nlp, x, c)

Evaluate the nonlinear constraints at x in place.

c = consH_nln(nlp, x, c)

Evaluate the nonlinear constraints at x.

decrement!(nlp, s)

Decrement counter s of problem nlp.

Hv = hGprod!(nlp, x, y, v, Hv)

Evaluate the product of the Lagrangian Hessian at (x,y) with the vector v in place.

Hv = hGprod(nlp, x, y, v)

Evaluate the product of the Lagrangian Hessian at (x,y) with the vector v.

Hv = hHprod!(nlp, x, y, v, Hv)

Evaluate the product of the Lagrangian Hessian at (x,y) with the vector v in place.

Hv = hHprod(nlp, x, y, v)

Evaluate the product of the Lagrangian Hessian at (x,y) with the vector v.

Hx = hessG(nlp, x, y)

Evaluate the Lagrangian Hessian at (x,y) as a sparse matrix. A Symmetric object wrapping the lower triangle is returned.

vals = hessG_coord!(nlp, x, y, vals)

Evaluate the Lagrangian Hessian at (x,y) in sparse coordinate format, overwriting vals. Only the lower triangle is returned.

vals = hessG_coord(nlp, x, y)

Evaluate the Lagrangian Hessian at (x,y) in sparse coordinate format. Only the lower triangle is returned.

H = hessG_op!(nlp, x, y, Hv)

Return the Lagrangian Hessian at (x,y) with objective function scaled by obj_weight as a linear operator, and storing the result on Hv. The resulting object may be used as if it were a matrix, e.g., w = H * v. The vector Hv is used as preallocated storage for the operation.

H = hessG_op(nlp, x, y)

Return the Lagrangian Hessian at (x,y) as a linear operator. The resulting object may be used as if it were a matrix, e.g., H * v.

hessG_structure!(nlp, rows, cols)

Return the structure of the Lagrangian Hessian in sparse coordinate format in place.

(rows,cols) = hessG_structure(nlp)

Return the structure of the Lagrangian Hessian in sparse coordinate format.

Hx = hessH(nlp, x, y)

Evaluate the Lagrangian Hessian at (x,y) as a sparse matrix. A Symmetric object wrapping the lower triangle is returned.

vals = hessH_coord!(nlp, x, y, vals)

Evaluate the Lagrangian Hessian at (x,y) in sparse coordinate format, overwriting vals. Only the lower triangle is returned.

vals = hessH_coord(nlp, x, y)

Evaluate the Lagrangian Hessian at (x,y) in sparse coordinate format. Only the lower triangle is returned.

H = hessH_op!(nlp, x, y, Hv)

Return the Lagrangian Hessian at (x,y) with objective function scaled by obj_weight as a linear operator, and storing the result on Hv. The resulting object may be used as if it were a matrix, e.g., w = H * v. The vector Hv is used as preallocated storage for the operation.

H = hessH_op(nlp, x, y)

Return the Lagrangian Hessian at (x,y) as a linear operator. The resulting object may be used as if it were a matrix, e.g., H * v.

hessH_structure!(nlp, rows, cols)

Return the structure of the Lagrangian Hessian in sparse coordinate format in place.

(rows,cols) = hessH_structure(nlp)

Return the structure of the Lagrangian Hessian in sparse coordinate format.

increment_cc!(nlp, s)

Increment counter s of problem nlp.

J = jG_op!(nlp, x, Jv, Jtv)

Return the Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

Jv = jGprod!(nlp, x, v, Jv)

Evaluate $J(x)v$, the Jacobian-vector product at x in place.

JGv = jGprod!(nlp, x, v, Jv) Evaluate $∇G(x)v$, the Jacobian-vector product at x in place.

Jv = jGprod(nlp, x, v)

Evaluate $J(x)v$, the Jacobian-vector product at x.

Jv = jGprodlin!(nlp, x, v, Jv)

Evaluate $J(x)v$, the linear Jacobian-vector product at x in place.

Jv = jGprodlin(nlp, x, v)

Evaluate $J(x)v$, the linear Jacobian-vector product at x.

Jv = jGprodnln!(nlp, x, v, Jv)

Evaluate $J(x)v$, the nonlinear Jacobian-vector product at x in place.

Jv = jGprodnln(nlp, x, v)

Evaluate $J(x)v$, the nonlinear Jacobian-vector product at x.

Jtv = jGtprod!(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product at x in place. If the problem has linear and nonlinear constraints, this function allocates.

Jtv = jtprodG(nlp, x, v, Jtv)

Evaluate $∇G(x)^Tv$, the transposed-Jacobian-vector product at x

Jtv = jGtprod(nlp, x, v)

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product at x.

Jtv = jGtprodlin!(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the linear transposed-Jacobian-vector product at x in place.

Jtv = jGtprodlin(nlp, x, v)

Evaluate $J(x)^Tv$, the linear transposed-Jacobian-vector product at x.

Jtv = jGtprodnln!(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the nonlinear transposed-Jacobian-vector product at x in place.

Jtv = jGtprodnln(nlp, x, v)

Evaluate $J(x)^Tv$, the nonlinear transposed-Jacobian-vector product at x.

J = jH_op!(nlp, x, Jv, Jtv)

Return the Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

Jv = jHprod!(nlp, x, v, Jv)

Evaluate $J(x)v$, the Jacobian-vector product at x in place.

JHv = jHprod!(nlp, x, v, Jv) Evaluate $∇H(x)v$, the Jacobian-vector product at x in place.

Jv = jHprod(nlp, x, v)

Evaluate $J(x)v$, the Jacobian-vector product at x.

Jv = jHprodlin!(nlp, x, v, Jv)

Evaluate $J(x)v$, the linear Jacobian-vector product at x in place.

Jv = jHprodlin(nlp, x, v)

Evaluate $J(x)v$, the linear Jacobian-vector product at x.

Jv = jHprodnln!(nlp, x, v, Jv)

Evaluate $J(x)v$, the nonlinear Jacobian-vector product at x in place.

Jv = jHprodnln(nlp, x, v)

Evaluate $J(x)v$, the nonlinear Jacobian-vector product at x.

Jtv = jHtprod!(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product at x in place. If the problem has linear and nonlinear constraints, this function allocates.

Jtv = jtprodH(nlp, x, v, Jtv)

Evaluate $∇H(x)^Tv$, the transposed-Jacobian-vector product at x

Jtv = jHtprod(nlp, x, v)

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product at x.

Jtv = jHtprodlin!(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the linear transposed-Jacobian-vector product at x in place.

Jtv = jHtprodlin(nlp, x, v)

Evaluate $J(x)^Tv$, the linear transposed-Jacobian-vector product at x.

Jtv = jHtprodnln!(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the nonlinear transposed-Jacobian-vector product at x in place.

Jtv = jHtprodnln(nlp, x, v)

Evaluate $J(x)^Tv$, the nonlinear transposed-Jacobian-vector product at x.

Jx = jacG(nlp, x)

Evaluate $J(x)$, the constraints Jacobian at x as a sparse matrix.

vals = jacG_coord!(nlp, x, vals)

Evaluate $J(x)$, the constraints Jacobian at x in sparse coordinate format, rewriting vals.

vals = jacG_coord(nlp, x)

Evaluate $J(x)$, the constraints Jacobian at x in sparse coordinate format.

vals = jacG_lin_coord!(nlp, x, vals)

Evaluate $J(x)$, the linear constraints Jacobian at x in sparse coordinate format, overwriting vals.

vals = jacG_lin_coord(nlp, x)

Evaluate $J(x)$, the linear constraints Jacobian at x in sparse coordinate format.

J = jacG_lin_op!(nlp, x, Jv, Jtv)

Return the linear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

J = jacG_lin_op(nlp, x)

Return the linear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

jacG_lin_structure!(nlp, rows, cols)

Return the structure of the linear constraints Jacobian in sparse coordinate format in place.

(rows,cols) = jacG_lin_structure(nlp)

Return the structure of the linear constraints Jacobian in sparse coordinate format.

vals = jacG_nln_coord!(nlp, x, vals)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x in sparse coordinate format, overwriting vals.

vals = jacG_nln_coord(nlp, x)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x in sparse coordinate format.

J = jacG_nln_op!(nlp, x, Jv, Jtv)

Return the nonlinear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

J = jacG_nln_op(nlp, x)

Return the nonlinear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

jacG_nln_structure!(nlp, rows, cols)

Return the structure of the nonlinear constraints Jacobian in sparse coordinate format in place.

(rows,cols) = jacG_nln_structure(nlp)

Return the structure of the nonlinear constraints Jacobian in sparse coordinate format.

J = jacG_op(nlp, x)

Return the Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

jacG_structure!(nlp, rows, cols)

Return the structure of the constraints Jacobian in sparse coordinate format in place.

(rows,cols) = jacG_structure(nlp)

Return the structure of the constraints Jacobian in sparse coordinate format.

Jx = jacH(nlp, x)

Evaluate $J(x)$, the constraints Jacobian at x as a sparse matrix.

vals = jacH_coord!(nlp, x, vals)

Evaluate $J(x)$, the constraints Jacobian at x in sparse coordinate format, rewriting vals.

vals = jacH_coord(nlp, x)

Evaluate $J(x)$, the constraints Jacobian at x in sparse coordinate format.

vals = jacH_lin_coord!(nlp, x, vals)

Evaluate $J(x)$, the linear constraints Jacobian at x in sparse coordinate format, overwriting vals.

vals = jacH_lin_coord(nlp, x)

Evaluate $J(x)$, the linear constraints Jacobian at x in sparse coordinate format.

J = jacH_lin_op!(nlp, x, Jv, Jtv)

Return the linear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

J = jacH_lin_op(nlp, x)

Return the linear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

jacH_lin_structure!(nlp, rows, cols)

Return the structure of the linear constraints Jacobian in sparse coordinate format in place.

(rows,cols) = jacH_lin_structure(nlp)

Return the structure of the linear constraints Jacobian in sparse coordinate format.

vals = jacH_nln_coord!(nlp, x, vals)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x in sparse coordinate format, overwriting vals.

vals = jacH_nln_coord(nlp, x)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x in sparse coordinate format.

J = jacH_nln_op!(nlp, x, Jv, Jtv)

Return the nonlinear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

J = jacH_nln_op(nlp, x)

Return the nonlinear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

jacH_nln_structure!(nlp, rows, cols)

Return the structure of the nonlinear constraints Jacobian in sparse coordinate format in place.

(rows,cols) = jacH_nln_structure(nlp)

Return the structure of the nonlinear constraints Jacobian in sparse coordinate format.

J = jacH_op(nlp, x)

Return the Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

jacH_structure!(nlp, rows, cols)

Return the structure of the constraints Jacobian in sparse coordinate format in place.

(rows,cols) = jacH_structure(nlp)

Return the structure of the constraints Jacobian in sparse coordinate format.

neval_consG(nlp)

Get the number of consG evaluations.

neval_consG_lin(nlp)

Get the number of consG evaluations.

neval_consG_nln(nlp)

Get the number of consG evaluations.

neval_consH(nlp)

Get the number of consH evaluations.

neval_consH_lin(nlp)

Get the number of consH evaluations.

neval_consH_nln(nlp)

Get the number of consH evaluations.

neval_hGprod(nlp)

Get the number of hGprod evaluations.

neval_hHprod(nlp)

Get the number of hHprod evaluations.

neval_hessG(nlp)

Get the number of hessG evaluations.

neval_hessH(nlp)

Get the number of hessH evaluations.

neval_jGprod(nlp)

Get the number of jGprod evaluations.

neval_jGprod_lin(nlp)

Get the number of jGprod evaluations.

neval_jGprod_nln(nlp)

Get the number of jGprod evaluations.

neval_jGtprod(nlp)

Get the number of jGtprod evaluations.

neval_jGtprod_lin(nlp)

Get the number of jGtprod evaluations.

neval_jGtprod_nln(nlp)

Get the number of jGtprod evaluations.

neval_jHprod(nlp)

Get the number of jHprod evaluations.

neval_jHprod_lin(nlp)

Get the number of jHprod evaluations.

neval_jHprod_nln(nlp)

Get the number of jHprod evaluations.

neval_jHtprod(nlp)

Get the number of jHtprod evaluations.

neval_jHtprod_lin(nlp)

Get the number of jHtprod evaluations.

neval_jHtprod_nln(nlp)

Get the number of jHtprod evaluations.

neval_jacG(nlp)

Get the number of jacG evaluations.

neval_jacG_lin(nlp)

Get the number of jacG evaluations.

neval_jacG_nln(nlp)

Get the number of jacG evaluations.

neval_jacH(nlp)

Get the number of jacH evaluations.

neval_jacH_lin(nlp)

Get the number of jacH evaluations.

neval_jacH_nln(nlp)

Get the number of jacH evaluations.

c = viol!(nlp, x, c)
Return the vector of the constraints
lx <= x <= ux
lc <= c(x) <= uc,
lccG <= G(x),
lccH <= H(x),
G(x) .* H(x) <= 0

c = viol(nlp, x)

Evaluate $c(x)$, the constraints at x.

Return the violation of the constraints lb <= x <= ub, lc <= c(x) <= uc, lccG <= G(x), lccH <= H(x), G(x).*H(x) <= 0.