Line Search Parameters¶

wolfe1¶

Real value in (0,0.5]. Default value: 1e-4

First weak Wolfe line search parameter, ensuring sufficient decrease of the objective/penalty.

wolfe2¶

Real value in [wolfe1,1). Default value: 0.5

Second weak Wolfe line search parameter, ensuring algebraic increase in projected gradient.

linesearch_nondescent_maxit¶

Non-negative integer. Default value: 0

If the computed direction is not numerically a descent direction, the line search can still be optionally attempted to see if it gets “lucky”, using up to linesearch_nondescent_maxit evaluations of the penalty/objective function (since there may be numerical issues in calculating whether it truly is a descent direction or not).

linesearch_reattempts¶

Positive integer. Default value: 10

If the line search fails to bracket a minimizer, this may be an indication that the objective function is unbounded below. For constrained problems, it may be that the objective is only unbouded below off the feasible set, in which case lower values of the penalty parameter mu may be necessary for NCVX to find the feasible region. For constrained problems, if the line search fails to bracket a minimizer, NCVX will reattempt the line search with progressively lower values of mu, up to linesearch_reattempts times. See opts.linesearch_c_mu, opts.linesearch_reattempts_x0, and opts.linesearch_c_mu_x0. NOTE: this option is irrelevant for unconstrained problems.

linesearch_reattempts_x0¶

Positive integer. Default value: 30

The same as linesearch_reattempts but applies only to the first iteration, where it may beneficial to be more aggressive in lowering the penalty parameter for line search reattempts. NOTE: this option is irrelevant for unconstrained problems.

linesearch_c_mu¶

Real value in (0,1). Default value: 0.5

If the line search fails to bracket a minimizer for a constrained problem, and linesearch_reattempts > 0, each line search reattempt will try a progressively smaller penalty parameter, shrinking it by another factor of linesearch_c_mu on each reattempt. See opts.linesearch_reattempts, opts.linesearch_reattempts_x0, and opts.linesearch_c_mu_x0. NOTE: this option is irrelevant for unconstrained problems.

linesearch_c_mu_x0¶