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User Interface to Solve the Optimization Problem

The solver requires a set of parameters. Thereafter, we can just run the solver using the problem defined by the augmented lagrangian.

Solver Parameters

The solver has many knobs. The recommended settings are below:

using TrajOptSOCPs; #hide
currSolveParams = solverParams(0.1, 0.5,
                                8, 10,
                                10^-4,
                                10, 10^6,
                                2.5, 2, 0.2, 0.2, 0.4)
TrajOptSOCPs.solParamPrint(currSolveParams)

For more information, see

TrajOptSOCPs.solverParams — Type

Line Search Parameters (Notation from Toussaint Notes (2020))

paramA::Float16 # Used in Line Search, should be [0.01, 0.3]

paramB::Float16 # Used in Line Search, should be [0.1, 0.8]

Iteration Counter Parameters

maxOuterIters::Int32 # Number of Outer Loop iterations

maxNewtonSteps::Int32 # Number of Newton Steps per Outer Loop iterations

Exit Condition Parameter

rTol::Float64 # When steps are within rTol, loop will stop.

Penalty Update Parameters

penaltyStep::Float16 # Multiplies the penalty parameter per outer loop

penaltyMax::Float64 # Maximum value of the penalty parameter

Trust Region Parameters (Notation from Nocedal et Yuan (1998))

trSizeStart::Float32 # Starting size of the trust region

trc1::Float16 # Success Size Increase Parameter (1 < c1)

trc2::Float16 # Taylor Series Error Parameter (0 < c2 < 1)

trc3::Float16 # Failed Size Reduction Parameter (0 < c3 < c4)

trc4::Float16 # Failed Size Reduction Parameter (c3 < c4 < 1)

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Solve it!

At last, we can solve the problem!

# Initialize the primal-dual vector
# initTraj is from the rocket guess trajectory
# lambdaInit is from the dynamics constraints
initTrajPD = [initTraj; lambdaInit]

trajLambdaSolved, resArr = ALPrimalNewtonMain(initTrajPD, alRocket, currSolveParams)

For more information, see

TrajOptSOCPs.ALPrimalNewtonMain — Function
ALPrimalNewtonMain(y0, al::augLag, sp::solverParams)

Performs a maximum on N outer steps as specified by solverParams. May return early if the residual is lower than the tolerance specified by solverParams and the constraint penalty is high enough.

The function operates on an augmented lagrangian (AL) with primals (P) only (as opposed to a Primal-Dual set-up) for second-order cone programs (SOCP). See newtonTRLS_ALP for more information on the Newton Steps

returns (yStates, residuals) which are:

  • yStates: An array with one entry of the primal vector per Newton step
  • residuals: An array with one entry of the residual vector per Newton step

See also: augLag

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