API: Algorithms

SCvx*

Main.SCPLib.penalty — Method

Augmented Lagrangian penalty function

Main.SCPLib.solve! — Method

Solve non-convex OCP with SCvx* algorithm

Arguments

algo::SCvxStar: algorithm struct
prob::OptimalControlProblem: problem struct
x_ref: reference state history, size nx-by-N
u_ref: reference control history, size nu-by-N-1
maxiter::Int: maximum number of iterations
tol_feas::Float64: feasibility tolerance
tol_opt::Float64: optimality tolerance
tol_J0::Real: objective tolerance
verbosity::Int: verbosity level
store_iterates::Bool: whether to store iterates

Main.SCPLib.update_trust_region! — Method

Update trust-region size

Main.SCPLib.SCvxStar — Type

SCvx* algorithm

Arguments

nx::Int: number of states
N::Int: number of time steps
ng::Int: number of non-convex equality constraints
nh::Int: number of non-convex inequality constraints
Δ0::Float64: initial trust-region size
w0::Float64: initial penalty weight
rhos::Tuple{Real,Real,Real}: trust-region acceptance thresholds
alphas::Tuple{Real,Real}: trust-region size update factors
Δ_bounds::Tuple{Float64,Float64}: trust-region size bounds
gamma::Float64: stationarity tolerance update factor
beta::Float64: penalty weight update factor
w_max::Float64: maximum penalty weight

Main.SCPLib.SCvxStarSolution — Type

Solution struct for SCvx* algorithm

Prox-linear method

Main.SCPLib.solve! — Method

Solve non-convex OCP with prox-linear algorithm

Arguments

algo::ProxLinear: algorithm struct
prob::OptimalControlProblem: problem struct
x_ref: reference state history, size nx-by-N
u_ref: reference control history, size nu-by-N-1
maxiter::Int: maximum number of iterations
tol_feas::Float64: feasibility tolerance
tol_opt::Float64: optimality tolerance
tol_J0::Real: objective tolerance
verbosity::Int: verbosity level
store_iterates::Bool: whether to store iterates

Main.SCPLib.ProxLinear — Type

Prox-linear algorithm

The weights are defined such that the penalized objective of the subproblems are:

\[L(Z) + w_ep * ||G(Z) + ∇G(Z_ref)*(Z - Z_ref)||_1 + w_prox/2 * ||Z - Z_ref||_2^2\]

where L(Z) is the original objective function, G(Z) are the non-convex constraints.

Arguments

w_ep::Float64: exact penalty term weight
w_prox::Float64: proximal term weight
proximal_u::Bool: whether to enforce proximal constraint on u

Main.SCPLib.ProxLinearSolution — Type

Solution struct for prox-linear algorithm

Fixed trust-region/weight

Main.SCPLib.penalty — Method

Augmented Lagrangian penalty function

Main.SCPLib.solve! — Method

Solve non-convex OCP with fixed trust-region-weight SCP Algorithm

This algorithm employs a fixed trust-region & accepts every convex subproblem step. Artificial infeasibility is avoided by introducing slack variables for nonlinear constraints that are penalized quadratically with a fixed weight.

Arguments

algo::FixedTRWSCP: algorithm struct
prob::OptimalControlProblem: problem struct
x_ref: reference state history, size nx-by-N
u_ref: reference control history, size nu-by-N-1
maxiter::Int: maximum number of iterations
tol_feas::Float64: feasibility tolerance
tol_opt::Float64: optimality tolerance
tol_J0::Real: objective tolerance
verbosity::Int: verbosity level
store_iterates::Bool: whether to store iterates