| Option Name | MPL Name | Solver Param | ParamNr | Type | Default | Min | Max |
|---|---|---|---|---|---|---|---|
| Minimal box width | GOPTolMinWidthBox | GOP_BoxTol | 402 | real | 1e-6 | 0 | MAXREAL |
| Maximum box width | GOPTolMaxWidthBox | GOP_WidTol | 403 | real | 1e-4 | 0 | MAXREAL |
| Delta convexification tolerance | GOPTolDelta | GOP_DeltaTol | 404 | real | -1 | -1 | MAXINT |
| Certify global optimality | GOPCertifyGlobalOpt | GOP_OptChkMd | 407 | real | 1e-4 | 0 | MAXREAL |
| Use maximum width | GOPMaxWidthFlag | GOP_MaxWidMd | 409 | flag | 0 | 0 | 1 |
| GOP branching strategy | GOPBranching | GOP_BranchMd | 408 | list | 5 | 0 | 5 |
| GOP presolve level | GOPPresolve | GOP_PreLevel | 410 | list | 1022 | 0 | 1022 |
| GOP post-solving level | GOPPostSolving | GOP_PostLevel | 411 | int | 6 | 0 | 6 |
| GOP node selection | GOPNodeSelection | GOP_BBSrchMd | 412 | list | 1 | 0 | 1 |
| GOP decomposition | GOPDecompositionRule | GOP_DecompPtMd | 413 | list | 1 | 0 | 1 |
| GOP Algebraic reformulation | GOPAlgebraicReform | GOP_AlgReformMd | 414 | list | 18 | 0 | 30 |
| GOP Rounding | GOPReliableRounding | GOP_RelBrndMd | 415 | list | 0 | 0 | 6 |
| GOP Use bound limits | GOPUseBoundLimit | GOP_UseBndLim | 417 | list | 1 | 0 | 2 |
| GOP branch and bound | GOPBandBStrategy | GOP_CoreLevel | 419 | list | 30 | 0 | 32 |
| GOP Optimization mode | GOPOptimizationMode | GOP_Opt_Mode | 420 | list | 1 | 0 | 2 |
| GOP Heuristic mode | GOPHeuristicMode | GOP_Heu_Mode | 421 | flag | 0 | 0 | 1 |
| GOP new solution branching limit | GOPNewSolBranchLimit | GOP_LSolBranLim | 424 | int | -1 | -1 | MAXINT |
| Use global optimizer | UseGlobalOptimizer | flag | 0 | 0 | 1 |
This value specifies the minimal width of variable intervals in a box allowed to branch. The default value is 1.0e-6.
This value specifies the maximal width of variable intervals for a box to be considered as an incumbent box containing an incumbent solution.
This value is the delta tolerance in the GOP convexification. It is a measure of how closely the additional constraints added as part of convexification should be satisfied. The default value is 1e-7.
This specifies the criterion used to certify the global optimality. When this value is 0, the absolute deviation of objective lower and upper bounds should be smaller than GOP optimality tolerance at the global optimum. When its value is 1, the relative deviation of objective lower and upper bounds should be smaller than GOP optimality tolerance at the global optimum. The default value is 2, which means both absolute and relative tolerances are satisfied at global optimum.
This is the maximum width flag for the global solution. The GOP branch and bound may continue contracting a box with an incumbent solution until its maximum width is smaller than maximum box width. The possible value of 1 means the maximum width criterion is performed and 0 means the maximum width criterion is suppressed. The default value is 0.
This specifies the direction to branch first when branching on a variable. The branch variable is selected as the one that holds the largest magnitude in the measure. Possible values are:
| Absolute width (0) | Uses absolute width. |
| Locally relative width (1) | Uses locally relative width. |
| Globally relative width (2) | Uses globally relative width. |
| Globally relative distance (3) | Uses globally relative distance from the convex minimum to the bounds. |
| Absolute violation (4) | Absolute violation between the function and its convex envelope at the convex minimum. |
| Relative violation (5) | Relative violation between the function and its convex envelope at the convex minimum. |
This controls the amount and type of GOP pre-solving. Possible options are:
| Initial local optimization (2) | |
| Initial linear constraint propagation (4) | |
| Recursive linear constraint propagation (8) | |
| Recursive nonlinear constraint propagation (16) | |
| Search for good near feasible solutions (32) | |
| Check for unboundedness (64) | |
| Alter derivative methods (128) | |
| MIP pre-optimizations (256) | |
| NLP pre-optimizations (512) |
This controls the amount and type of GOP post-solving. The default value is 6 which will reoptimize variable bounds.
This specifies the node selection rule for choosing between all active nodes in the GOP branch-and-bound tree when solving global optimization programs. Possible selections are:
| Depth first search (0) | Uses depth first approach during the branch and bound phase. |
| Worst bound (1) | Selects node with the worst bound. |
This specifies the decomposition point selection rule. In the branch step of GOP branch-and-bound, a branch point M is selected to decompose the selected variable interval [Lb, Ub] into two subintervals, [Lb, M] and [M, Ub]. Possible options are:
| Mid-point (0) | Uses selection rule based on mid-points. |
| Convex minimum (1) | Based on local or convex minimum. |
This controls the algebraic reformulation rule for a GOP. The algebraic reformulation and analysis is very crucial in building a tight convex envelope to enclose the nonlinear/nonconvex functions. A lower degree of overestimation on convex envelopes helps increase the convergence rate to the global optimum. Possible options are:
| Rearrange (2) | Rearranges and collects terms. |
| Full expansion (4) | Expands all parentheses |
| Retain (8) | Retains nonlinear functions. |
| Selective expansion (16) | Selectively expands parentheses. |
This controls the reliable rounding rule in the GOP branch-and-bound. The global solver applies many sub optimizations to estimate the lower and upper bounds on the global optimum. A rounding error or numerical instability could unintentionally cut off a good solution. A variety of reliable approaches are available to improve the precision. Thought the default setting does not use any of these routines.
| Small tolerances (2) | Use smaller optimality/feasibility tolerances and appropriate presolving options. |
| Interval arithmetic (4) | Apply interval arithmetic to verify the solution feasibility. |
This value is a flag for the parameter GOP bound limit". Possible values are:
| Not used (0) | Does not use the bound limit on the variables. |
| In start (1) | Use the bound limit right at the beginning of global optimization. |
| After start (2) | Use the bound limit after the initial local optimization, if selected. This properly sets the bound limit for each variable to include the initial solution, if any, within the range. |
This controls the strategy of GOP branch-and-bound procedure. Possible options are:
| LP convex (2) | Uses LP convex relaxations. |
| Honor NLP solutions (4) | Honors NLP solutions. |
| Box branching (8) | Uses box branching. |
| Honor IPM solutions (16) | Honors IPM solutions. |
This specifies the mode for global search. Possible values are
| Feasible solution (0) | Does global search for a feasible solution. |
| Optimal solution (1) | Does global search for an optimal solution. |
| Unboundedness (2) | Does global search for an unbounded solution. |
This flag specifies if the heuristic is used in the global solver to find good solution. The default is off.
This value controls the branch limit until finding a new nonlinear solution since the last nonlinear solution is found. The default value is -1, which means no branch limit is imposed.
Boolean option that determines whether one wants the solve the NLP model with LINDO's global solver. The default is set to off.