QPSMPGP

Modified proportioning with (reduced) gradient projections type algorithm This method does three types of steps, unconstrained minimization if feasible, expansion step to expand the active set, and proportioning step to reduce the active set.

Options Database Keys

-qps_mpgp_alpha_direct - true sets expansion step length value directly, false (default) multiplier (typical between (0,2]) for step length equal to reciprocal of maximal eigenvalue
-qps_mpgp_alpha - fixed step length value for expansion, default: 2.0
-qps_mpgp_gamma - proportionality constant
-qps_mpgp_maxeig - approximate maximum eigenvalue of the Hessian (automatically computed by default)
-qps_mpgp_maxeig_tol - relative tolerance for power method to find approximate maximum eigenvalue of the Hessian
-qps_mpgp_maxeig_iter - number of iterations of power method to find an approximate maximum eigenvalue of the Hessian
-qps_mpgp_btol - boundary overshoot tolerance, default: 10*PETSC_MACHINE_EPSILON"
-qps_mpgp_bound_chop_tol - sets boundary to 0 for |boundary|<tol, default: 0
-qps_mpgp_expansion_type - set expansion step type, default: "std"
-qps_mpgp_expansion_length_type - set expansion step length type, default: "fixed"
-qps_mpgp_alpha_reset - if alpha=Nan reset to initial value, otherwise keep last alpaha, default: true
-qps_mpgp_fallback - throw away expansion step if cost function increased and do a std expansion step, default false
-qps_mpgp_fallback2 - same as fallback which is done only if the next step is proportioning

Available expansion types

"std" - standard expansion
"projcg" - unconstrained CG step projected back to feasible set
"gf" - free gradient for both step length computation and expansion direction
"g" - normal gradient for both step length computation and expansion direction
"gfgr" - expansion in free gradient direction, steplength using reduced gradient
"ggr" - expansion in normal gradient direction, steplength using reduced gradient

Available step lengths types

"fixed" - standard fixed step length
"opt" - optimal step length
"optapprox" - (usually poor) approximation of optimal step length
"bb" - Barzilai-Borwein step length

Reference

. J. Kružík, D. Horák, M. Čermák, L. Pospíšil, M. Pecha, "Active set expansion strategies in MPRGP algorithm", Advances in Engineering Software, Volume 149, 2020.

See Also

QPSCreate(), QPSSetType(), QPSType (for list of available types), QPS,
QPSMPGPSetAlpha(), QPSMPGPGetAlpha(), QPSMPGPSetGamma(), QPSMPGPGetGamma(), QPSMPGPGetOperatorMaxEigenvalue(), QPSMPGPSetOperatorMaxEigenvalue(), QPSMPGPUpdateMaxEigenvalue(), QPSMPGPSetOperatorMaxEigenvalueTolerance(), QPSMPGPGetOperatorMaxEigenvalueTolerance(), QPSMPGPGetOperatorMaxEigenvalueIterations(), QPSMPGPSetOperatorMaxEigenvalueIterations(), QPSMPGPGetCurrentStepType()

Level

intermediate

Location

src/qps/impls/mpgp/mpgp.c
Index of all QPS routines
Table of Contents for all manual pages
Index of all manual pages