Information

The information constants describe the relevant information of the model components (objective function, constraints and variables), solution results, and feasibility relaxation calculation results. This chapter will introduce the information constants provided by COPT and their meanings.

Table 16 COPT Information

Name	Type	Description
Obj	Double	Objective cost of columns
LB	Double	Lower bounds of columns or rows
UB	Double	Upper bounds of columns or rows
Value	Double	Solution of columns
Slack	Double	Solution of slack variables, also known as activities of constraints. Only available for LP problem
Dual	Double	Solution of dual variables. Only available for LP problem
RedCost	Double	Reduced cost of columns. Only available for LP problem
SAObjLow	Double	Indicates the minimum value to which the objective coefficient of a variable can be reduced while keeping the current basis optimal
SAObjUp	Double	Indicates the maximum value to which the objective coefficient of a variable can be increased while keeping the current basis optimal
SALBLow	Double	Indicates the minimum value to which the lower bound of the variable/constraint can be reduced while keeping the current basis optimal
SALBUp	Double	Indicates the maximum value to which the lower bound of the variable/constraint can be increased while keeping the current basis optimal
SAUBLow	Double	Indicates the minimum value to which the upper bound of the variable/constraint can be reduced while keeping the current basis optimal
SAUBUp	Double	Indicates the maximum value to which the upper bound of the variable/constraint can be increased while keeping the current basis optimal
DualFarkas	Double	The dual Farkas for constraints of an infeasible LP problem
PrimalRay	Double	The primal ray for variables of an unbounded LP problem
RelaxLB	Double	Feasibility relaxation values for lower bounds of columns or rows
RelaxUB	Double	Feasibility relaxation values for upper bounds of columns or rows
RelaxValue	Double	Solutions for the original model variables (columns) in the feasibility relaxation model

Table 17 COPT Callback Information

Name	Type	Description
BestObj	Double	Current best objective
BestBnd	Double	Current best objective bound
HasIncumbent	Integer	Whether an incumbent is available
Incumbent	Double	Current best feasible solution
MipCandObj	Double	Objective value for current feasible solution candidate
MipCandidate	Double	Current feasible solution candidate
RelaxSolObj	Double	Current Objective of LP-relaxation
RelaxSolution	Double	Current solution of LP-relaxation
NodeStatus	Integer	The solution status of the LP-relaxation problem at the current node

Problem information

• Obj

  Double information.

  Objective cost of columns.

• LB

  Double information.

  Lower bounds of columns or rows.

• UB

  Double information.

  Upper bounds of columns or rows.

Solution and sensitivity analysis information

• Value

  Double information.

  Solution of columns.

• Slack

  Double information.

  Solution of slack variables, also known as activities of constraints. Only available for LP problem.

• Dual

  Double information.

  Solution of dual variables. Only available for LP problem.

• RedCost

  Double information.

  Reduced cost of columns. Only available for LP problem.

• SAObjLow

  Double information.

  Sensitivity analysis information of the objective coefficient.

  Indicates the minimum value to which the objective coefficient of a variable can be reduced while keeping the current basis optimal.

• SAObjUp

  Double information.

  Sensitivity analysis information of the objective coefficient.

  Indicates the maximum value to which the objective coefficient of a variable can be increased while keeping the current basis optimal.

• SALBLow

  Double information.

  Sensitivity analysis information of the lower bound of the variable/constraint.

  Indicates the minimum value to which the lower bound of the variable/constraint can be reduced while keeping the current basis optimal.

• SALBUp

  Double information.

  Sensitivity analysis information of the lower bound of the variable/constraint.

  Indicates the maximum value to which the lower bound of the variable/constraint can be increased while keeping the current basis optimal.

• SAUBLow

  Double information.

  Sensitivity analysis information of the upper bound of the variable/constraint.

  Indicates the minimum value to which the upper bound of the variable/constraint can be reduced while keeping the current basis optimal.

• SAUBUp

  Double information.

  Sensitivity analysis information of the upper bound of the variable/constraint.

  Indicates the maximum value to which the upper bound of the variable/constraint can be increased while keeping the current basis optimal.

Dual Farkas and primal ray

Advanced topic. When an LP is infeasible or unbounded, the solver can return the dual Farkas or primal ray to prove it.

• DualFarkas

  Double information.

  The dual Farkas for constraints of an infeasible LP problem. Please enable the parameter "ReqFarkasRay" to ensure that the dual Farkas is available when the LP is infeasible.

  Without loss of generality, the concept of the dual Farkas can be conveniently demonstrated using an LP problem with general variable bounds and equality constraints: \(Ax = 0 \text{ and } l \leq x \leq u\). When the LP is infeasible, a dual Farkas vector \(y\) can prove that the system has conflict that \(\max y^TAx < y^T b = 0\). Computing \(\max y^TAx\): with the vector \(\hat{a} = y^TA\), choosing variable bound \(x_i = l_i\) when \(\hat{a}_i < 0\) and \(x_i = u_i\) when \(\hat{a}_i > 0\) gives the maximal possible value of \(y^TAx\) for any \(x\) within their bounds.

  Some application relies on the alternate conflict \(\min \bar{y}^TAx > \bar{y}^T b = 0\). This can be achieved by negating the dual Farkas, i.e. \(\bar{y}=-y\) returned by the solver.

  In very rare cases, the solver may fail to return a valid dual Farkas. For example when the LP problem slightly infeasible by tiny amount, which We recommend to study and to repair the infeasibility using FeasRelax instead.

• PrimalRay

  Double information.

  The primal ray for variables of an unbounded LP problem. Please enable the parameter "ReqFarkasRay" to ensure that the primal ray is available when an LP is unbounded.

  For a minimization LP problem in the standard form: \(\min c^T x, Ax = b \text{ and } x \geq 0\), a primal ray vector \(r\) satisfies that \(r \geq 0, Ar = 0 \text{ and } c^T r < 0\).

Feasibility relaxation information

• RelaxLB

  Double information.

  Feasibility relaxation values for lower bounds of columns or rows.

• RelaxUB

  Double information.

  Feasibility relaxation values for upper bounds of columns or rows.

• RelaxValue

  Double information.

  Solutions for the original model variables (columns) in the feasibility relaxation model.

Callback information

• BestObj

  Double information.

  Current best objective.

• BestBnd

  Double information.

  Current best objective bound.

• HasIncumbent

  Integer information.

  Whether an incumbent is available.

• Incumbent

  Double information.

  Current best feasible solution.

• MipCandObj

  Double information.

  Objective value for current feasible solution candidate.

• MipCandidate

  Double information.

  Current feasible solution candidate.

• RelaxSolObj

  Double information.

  Current Objective of LP-relaxation.

• RelaxSolution

  Double information.

  Current solution of LP-relaxation.

• NodeStatus

  Integer information.

  The solution status of the LP-relaxation problem at the current node. For possible values, please refer to: General Constants Chapter: Solution Status (Part), except for NODELIMIT, UNSTARTED, INF_OR_UNB .

Methods for accessing information

In different programming interfaces, the ways to access and set information are slightly different. For details, please refer to the corresponding chapters for each programming language API:

• C API: C API Functions: Accessing information of problem

• C# API: C# API Reference: Information

• Java API: Java API Reference: Information

• Python API: Python API Reference: Information