OSQP settings sequence data frame

Data frame containing a sequence of OSQP settings for tsbalancing() specified with argument osqp_settings_df. The package includes two predefined OSQP settings sequence data frames:

• default_osqp_sequence: fast and effective (default osqp_settings_df argument value);

• alternate_osqp_sequence: geared towards precision at the expense of execution time.

See vignette("osqp-settings-sequence-dataframe") for the actual contents of these data frames.

Usage

# Default sequence:
# tsbalancing(..., osqp_settings_df = default_osqp_sequence)

# Alternative (slower) sequence:
# tsbalancing(..., osqp_settings_df = alternate_osqp_sequence)

# Custom-made sequence (use with caution!):
# tsbalancing(..., osqp_settings_df = <my-osqp-sequence-dataframe>)

# Single solving attempt with the default OSQP settings (not recommended!):
# tsbalancing(..., osqp_settings_df = NULL)

Format

A data frame with at least one row and at least one column, the most common columns being:

max_iter

Maximum number of iterations (integer)

sigma

Alternating direction method of multipliers (ADMM) sigma step (double)

eps_abs

Absolute tolerance (double)

eps_rel

Relative tolerance (double)

eps_prim_inf

Primal infeasibility tolerance (double)

eps_dual_inf

Dual infeasibility tolerance (double)

polish

Perform solution polishing (logical)

scaling

Number of scaling iterations (integer)

prior_scaling

Scale problem data prior to solving with OSQP (logical)

require_polished

Require a polished solution to stop the sequence (logical)

[any-other-OSQP-setting]

Value of the corresponding OSQP setting

Details

With the exception of prior_scaling and require_polished, all columns of the data frame must correspond to a OSQP setting. Default OSQP values are used for any setting not specified in this data frame. Visit https://osqp.org/docs/interfaces/solver_settings.html for all available OSQP settings. Note that the OSQP verbose setting is actually controlled through tsbalancing() arguments quiet and display_level (i.e., column verbose in a OSQP settings sequence data frame would be ignored).

Each row of a OSQP settings sequence data frame represents one attempt at solving a balancing problem with the corresponding OSQP settings. The solving sequence stops as soon as a valid solution is obtained (a solution for which all constraint discrepancies are smaller or equal to the tolerance specified with tsbalancing() argument validation_tol) unless column require_polished = TRUE, in which case a polished solution from OSQP (status_polish = 1) would also be required to stop the sequence. Constraint discrepancies correspond to \(\mathrm{max}(0, l - Ax, Ax - u)\) with constraints defined as \(l \le Ax \le u\). In the event where a satisfactory solution cannot be obtained after having gone through the entire sequence, tsbalancing() returns the solution that generated the smallest total constraint discrepancies among valid solutions, if any, or among all solutions, otherwise. Note that running the entire solving sequence can be enforced by specifying tsbalancing() argument full_sequence = TRUE. Rows with column prior_scaling = TRUE have the problem data scaled prior to solving with OSQP, using the average of the free (nonbinding) problem values as the scaling factor.

In addition to specifying a custom-made OSQP settings sequence data frame with argument osqp_settings_df, one can also specify osqp_settings_df = NULL which would result in a single solving attempt with default OSQP values for all settings along with prior_scaling = FALSE and require_polished = FALSE. Note that it is recommended, however, to first try data frames default_osqp_sequence and alternate_osqp_sequence, along with full_sequence = TRUE if necessary, before considering other alternatives.

Vignette OSQP Settings Sequence Data Frame (vignette("osqp-settings-sequence-dataframe")) contains additional information.