OpenSQP

The OpenSQP solver is a gradient-based optimization algorithm that uses sequential quadratic programming (SQP) to solve general nonlinear programming problems. It uses a damped BFGS algorithm to approximate the Hessian of the Lagrangian and an augmented Lagrangian merit function for the line search. The OpenSQP solver is fully implemented in modOpt. The source code is available here.

Note

For built-in algorithms like OpenSQP, there are no “solver-specific” options, as the entire solver is integrated within modOpt. As a result, all solver options are set directly using keyword arguments, rather than being passed separately in a solver_options dictionary as in other performant algorithms.

To use the OpenSQP solver, start by importing it as shown in the following code:

from modopt import OpenSQP

Options could be set by passing them as kwargs when instantiating the OpenSQP optimizer object. For example, we can set the maximum number of iterations maxiter and the optimality tolerance opt_tol shown below.

optimizer = OpenSQP(prob, maxiter=20, opt_tol=1e-8)

See the table below for the full list of options.

OpenSQP (solver) options

Option	Type (default value)	Description
recording	bool (False)	If True, records all outputs from the optimization. This needs to be enabled for hot-starting the same problem later, if the optimization is interrupted.
hot_start_from	str (None)	The record file from which to hot-start the optimization.
hot_start_atol	float (0.0)	The absolute tolerance check for the inputs when reusing outputs from the hot-start record.
hot_start_rtol	float (0.0)	The relative tolerance check for the inputs when reusing outputs from the hot-start record.
visualize	list ([])	The list of scalar variables to visualize during the optimization.
turn_off_outputs	bool (False)	If True, prevents modOpt from generating any output files.
verbosity	int (0)	If 0, suppresses all console outputs. If 1, prints various convergence measures and diagnostic messages.
maxiter	int (1000)	Maximum number of major iterations.
opt_tol	float(1e-7)	Optimality tolerance.
feas_tol	float (1e-7)	Feasibility tolerance. Terminate successfully only if the scaled maximum constraint violation is less than feas_tol.
aqp_primal_feas_tol	float (1e-8)	Tolerance for the primal feasibility of the augmented QP subproblem.
aqp_dual_feas_tol	float (1e-8)	Tolerance for the dual feasibility of the augmented QP subproblem.
aqp_time_limit	float (5.0)	Time limit for augmented QP solution in seconds.
ls_min_step	float (1e-14)	Minimum step size for the line search.
ls_max_step	float (1.0)	Maximum step size for the line search.
ls_maxiter	int (10)	Maximum number of iterations for the line search.
ls_eta_a	float (1e-4)	Armijo (sufficient decrease condition) parameter for the line search.
ls_eta_w	float (0.9)	Wolfe (curvature condition) parameter for the line search.
ls_alpha_tol	float (1e-14)	Relative tolerance for an acceptable step in the line search.
bfgs_init_lag_hess	np.ndarray (None)	Initial symmetric and positive definite approximation of the Lagrangian Hessian of shape (nx,nx) for the BFGS update. Available only with SciPy >= 1.14.0.
init_multipliers	dict (None)	Initial Lagrange multiplier values for the bounds and constraints. Should be a dict with keys ‘cl’, ‘cu’, ‘xl’, ‘xu’ corresponding to the lower and upper bounds of the constraints and variables, and values being arrays of the same length as the number of constraints or variables.
readable_outputs	list ([])	List of outputs to be written to readable text output files. Available outputs are: ‘major’, ‘obj’, ‘x’, ‘lag_mult’, ‘slacks’, ‘constraints’, ‘opt’, ‘feas’, ‘sum_viol’, ‘max_viol’, ‘time’, ‘nfev’, ‘ngev’, ‘step’, ‘rho’, ‘merit’, ‘elastic’, ‘gamma’, ‘low_curvature’.