VariationalInequalitySolver

vals = hess_coord_residual!(model, x, v, vals)

Computes the linear combination of the Hessians of the residuals at x with coefficients v in sparse coordinate format, rewriting vals.

vals = hess_coord_residual(model, x, v)

Computes the linear combination of the Hessians of the residuals at x with coefficients v in sparse coordinate format.

Hop = hess_op_residual(model, x, i)

Computes the Hessian of the i-th residual at x, in linear operator form.

H = hess_residual(model, x, v)

Computes the linear combination of the Hessians of the residuals at x with coefficients v. A Symmetric object wrapping the lower triangle is returned.

hess_structure_residual!(model, rows, cols)

Returns the structure of the residual Hessian in place.

(rows,cols) = hess_structure_residual(model)

Returns the structure of the residual Hessian.

Hiv = hprod_residual!(model, x, i, v, Hiv)

Computes the product of the Hessian of the i-th residual at x, times the vector v, and stores it in vector Hiv.

Hiv = hprod_residual(model, x, i, v)

Computes the product of the Hessian of the i-th residual at x, times the vector v.

vals = jac_coord_residual!(model, x, vals)

Computes the Jacobian of the residual at x in sparse coordinate format, rewriting vals. rows and cols are not rewritten.

(rows,cols,vals) = jac_coord_residual(model, x)

Computes the Jacobian of the residual at x in sparse coordinate format.

Jx = jac_op_residual!(model, rows, cols, vals, Jv, Jtv)

Computes $J(x)$, the Jacobian of the residual given by (rows, cols, vals), in linear operator form. The vectors Jv and Jtv are used as preallocated storage for the operations.

Jx = jac_op_residual(model, x)

Computes $J(x)$, the Jacobian of the residual at x, in linear operator form.

Jx = jac_residual(model, x)

Computes $J(x)$, the Jacobian of the residual at x.

(rows,cols) = jac_structure_residual!(model, rows, cols)

Returns the structure of the constraint's Jacobian in sparse coordinate format in place.

(rows,cols) = jac_structure_residual(model)

Returns the structure of the constraint's Jacobian in sparse coordinate format.

Jv = jprod_residual!(model, x, v, Jv)

Computes the product of the Jacobian of the residual at x and a vector, i.e., $J(x)v$, storing it in Jv.

Jv = jprod_residual!(model, rows, cols, vals, v, Jv)

Computes the product of the Jacobian of the residual given by (rows, cols, vals) and a vector, i.e., $J(x)v$, storing it in Jv.

Jv = jprod_residual(model, x, v)

Computes the product of the Jacobian of the residual at x and a vector, i.e., $J(x)v$.

Hj = jth_hess_residual(model, x, j)

Computes the Hessian of the j-th residual at x.

Jtv = jtprod_residual!(model, x, v, Jtv)

Computes the product of the transpose of the Jacobian of the residual at x and a vector, i.e., $J(x)^Tv$, storing it in Jtv.

Jtv = jtprod_residual!(model, rows, cols, vals, v, Jtv)

Computes the product of the transpose of the Jacobian of the residual given by (rows, cols, vals) and a vector, i.e., $J(x)^Tv$, storing it in Jv.

Jtv = jtprod_residual(model, x, v)

Computes the product of the transpose of the Jacobian of the residual at x and a vector, i.e., $J(x)^Tv$.

Fx = residual!(model, x, Fx)

Computes $F(x)$, the residual at x.

Fx = residual(model, x)

Computes $F(x)$, the residual at x.

Yura Malitsky. Projected reflected gradient methods for monotone variational inequalities. SIAM Journal on Optimization, 25(1):502–520, 2015.

project!(Px::AbstractVector{T}, model::VIModel, x::AbstractVector{T}) where {T}

Compute the projection of d over X in-place, i.e.,

\[ min_x 0.5 | d - x |²₂ s.t. x ∈ X\]

project(model::VIModel, x::AbstractVector{T}) where {T}

Compute the projection of d over X, i.e.,

\[ min_x 0.5 | d - x |²₂ s.t. x ∈ X\]

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