# Options for BonCouenne?

### Linearization options

convexification_cuts <num>

Specify the frequency (in terms of nodes) at which linearization cuts are generated. Default: 1. If 0, linearization cuts are never separated.

convexification_points <num>

Specify the number of points at which to convexify. Default: 1.

violated_cuts_only <yes|no>

If set to yes (default), only violated convexification cuts will be added.

art_lower <num>

Set artificial lower bound (for minimization problems),
useful when a lower bound is known or for testing purposes.
Default value is -10^{50}.

opt_window <num>

Multiplier for restricting variable bounds around known optimum (to be read from file with
method CouenneProblem::readOptimum()). If the optimal value x_{i} of the i-th variable is known,
before starting Couenne its bounds will be intersected with interval [x_{i}-K(1+|x_{i}|),x_{i}+K(1+|x_{i}|)],
where K is the value of the option. Default value is infinity.

use_quadratic <yes|no>

Use quadratic expressions and related exprQuad class. Still in testing, so default is "no".

### Bound tightening options

feasibility_bt <yes|no>

Use feasibility-based bound tightening (strongly recommended). Default value is "yes".

optimality_bt

Optimality-based (expensive) bound tightening. Only recommended for problems with few variables and/or at the initial nodes of the B&B tree. Default is "no". If set to "yes", we recommend to couple it with a value of log_num_obbt_per_level of 0 (see below).

log_num_obbt_per_level <num>

Specify the frequency (in terms of nodes) for optimality-based bound tightening. Default is 0.

- If -1, apply at every node (expensive!).
- If 0, apply at root node only.
- If k>0, apply with probability 2
^{(k - level)}, level being the current depth of the B&B tree.

aggressive_fbbt <yes|no"

Aggressive feasibility-based bound tightening (to use with NLP points). Default value is "yes". This is also computationally expensive.

log_num_abt_per_level <num>

Specify the frequency (in terms of nodes) for aggressive bound tightening (similar to log_num_obbt_per_level).

- If -1, apply at every node (expensive!);
- If 0, apply at root node only;
- If k>0, apply with probability 2
^{(k - level)}, level being the current depth of the B&B tree.

### Branching options

branch_fbbt <yes|no>

Apply bound tightening before branching. default: yes

branch_conv_cuts <yes|no>

Apply convexification cuts before branching (not active yet). Default: no.

branch_pt_select <string>

Chooses branching point selection strategy. Possible values are

- "lp-clamped": LP point clamped in [k,1-k] of the bound intervals (k defined by lp_clamp);
- "lp-central": LP point if within [k,1-k] of the bound intervals, middle point otherwise (k defined by branch_lp_clamp);
- "balanced": minimizes max distance from curve to convexification;
- "min-area": minimizes total area of the two convexifications;
- "mid-point": convex combination of current point and mid point;
- "no-branch": do not branch, return null infeasibility; for testing purposes only.

Default is mid-point.

branch_lp_clamp <num>

Defines a threshold for selecting an LP point as the branching point;
<num> is between 0 and 0.5 and defaults to 0.2. Suppose variable x_{i} with bounds [l_{i},u_{i}]
is chosen for branching. If the lp-central or lp-clamp strategies
are selected, the branching point is projected into the interval [L_{i},U_{i}] with
L_{i} = l_{i}+ a(u_{i} - l_{i}) and U_{i} = l_{i}+ (1-a)(u_{i} - l_{i}).

branch_midpoint_alpha <num>

Defines convex combination of mid point and current LP point: branching point will be
alpha x_{i} + (1-alpha) (l_{i}+u_{i})/2. Default value is 0.25.

Options `branch_pt_select` and `branch_lp_clamp` above are
also available for the following set of operators, and are applied to
each of these operators independently:
"prod", "div", "exp", "log", "trig", "pow", "negpow", "sqr", "cube".

For instance, the following settings:

branch_pt_select balanced branch_pt_select_prod lp-clamp branch_lp-clamp_prod 0.15 branch_pt_select_log lp-central branch_lp-clamp_log 0.1

specify balanced strategy for all operators except products and logarithms, lp-clamp with parameter 0.15 for products and lp-central with parameter 0.1 for logarithms.

### Upper bounding options

local_optimization_heuristic <yes|no>

Search for local solutions of NLPs. Default: yes.

log_num_local_optimization_per_level <num>

Specify the logarithm of the number of local optimizations to perform on average for each level of given depth of the tree.

If equal to -1, solve as many nlp's at the nodes for each level of the tree.

Nodes are randomly selected. If for a given level there are less nodes than this number nlp, are solved for every nodes. For example, if parameter is 8, nlp's are solved for all node until level 8, then for half the node at level 9, 1/4 at level 10.

art_cutoff <num>

Set artificial cutoff useful when a feasible solution is known or for testing purposes.
Default value is 10^{50}.

feas_tolerance

This is a feasibility tolerance for candidate feasible solutions.
Default value is 10^{-7}.