Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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Sequential Quadratic Program


This keyword is related to the topics:


Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Optional verify_level

Verify the quality of analytic gradients

Optional function_precision Specify the maximum precision of the analysis code responses
Optional linesearch_tolerance Choose how accurately the algorithm will compute the minimum in a line search
Optional convergence_tolerance

Stopping criterion based on convergence of the objective function or statistics

Optional max_iterations

Stopping criterion based on number of iterations

Optional constraint_tolerance The maximum allowable value of constraint violation still considered to be feasible
Optional speculative Compute speculative gradients
Optional max_function_evaluations Stopping criteria based on number of function evaluations
Optional scaling Turn on scaling for variables, responses, and constraints
Optional linear_inequality_constraint_matrix Define coefficients of the linear inequality constraints
Optional linear_inequality_lower_bounds Define lower bounds for the linear inequality constraint
Optional linear_inequality_upper_bounds Define upper bounds for the linear inequality constraint
Optional linear_inequality_scale_types Specify how each linear inequality constraint is scaled
Optional linear_inequality_scales Define the characteristic values to scale linear inequalities
Optional linear_equality_constraint_matrix Define coefficients of the linear equalities
Optional linear_equality_targets Define target values for the linear equality constraints
Optional linear_equality_scale_types Specify how each linear equality constraint is scaled
Optional linear_equality_scales Define the characteristic values to scale linear equalities
Optional model_pointer

Identifier for model block to be used by a method


NPSOL provides an implementation of sequential quadratic programming that can be accessed with npsol_sqp.

Stopping Criteria

The method independent controls for max_iterations and max_function_evaluations limit the number of major SQP iterations and the number of function evaluations that can be performed during an NPSOL optimization. The convergence_tolerance control defines NPSOL's internal optimality tolerance which is used in evaluating if an iterate satisfies the first-order Kuhn-Tucker conditions for a minimum. The magnitude of convergence_tolerance approximately specifies the number of significant digits of accuracy desired in the final objective function (e.g., convergence_tolerance = 1.e-6 will result in approximately six digits of accuracy in the final objective function). The constraint_tolerance control defines how tightly the constraint functions are satisfied at convergence. The default value is dependent upon the machine precision of the platform in use, but is typically on the order of 1.e-8 for double precision computations. Extremely small values for constraint_tolerance may not be attainable. The output verbosity setting controls the amount of information generated at each major SQP iteration: the silent and quiet settings result in only one line of diagnostic output for each major iteration and print the final optimization solution, whereas the verbose and debug settings add additional information on the objective function, constraints, and variables at each major iteration.


NPSOL is not a parallel algorithm and cannot directly take advantage of concurrent evaluations. However, if numerical_gradients with method_source dakota is specified, then the finite difference function evaluations can be performed concurrently (using any of the parallel modes described in the Users Manual [5]).

An important related observation is the fact that NPSOL uses two different line searches depending on how gradients are computed. For either analytic_gradients or numerical_gradients with method_source dakota, NPSOL is placed in user-supplied gradient mode (NPSOL's "Derivative Level" is set to 3) and it uses a gradient-based line search (the assumption is that user-supplied gradients are inexpensive). On the other hand, if numerical_gradients are selected with method_source vendor, then NPSOL is computing finite differences internally and it will use a value-based line search (the assumption is that finite differencing on each line search evaluation is too expensive). The ramifications of this are: (1) performance will vary between method_source dakota and method_source vendor for numerical_gradients, and (2) gradient speculation is unnecessary when performing optimization in parallel since the gradient-based line search in user-supplied gradient mode is already load balanced for parallel execution. Therefore, a speculative specification will be ignored by NPSOL, and optimization with numerical gradients should select method_source dakota for load balanced parallel operation and method_source vendor for efficient serial operation.

Linear constraints

Lastly, NPSOL supports specialized handling of linear inequality and equality constraints. By specifying the coefficients and bounds of the linear inequality constraints and the coefficients and targets of the linear equality constraints, this information can be provided to NPSOL at initialization and tracked internally, removing the need for the user to provide the values of the linear constraints on every function evaluation.