Error Messages/40699

Example text

 The shadow price (dual of constraints) is not available for non-linear problems.

 The shadow price (dual of constraints) can only be computed for an LP or QP with all linear constraints and 
 all continuous variables.


The LpShadow function can only be used to compute the shadow price (or dual value of constraints) for a linear program, or quadratic program with linear constraints, and all continuous variables, created via a call to LpDefine or QpDefine. It cannot be used with quadratic programs when quadratic constraints are present, or with NLPs, or when integer or grouped-integer decision variables are present.

The concept of a shadow price is meaningful in the context of a QCP or NLP with continuous variables, but not computed by this function. You could compute the shadow price of a QCP (i.e., with convex quadratic constraints), for example, by using:

 Var delta := 1e-6;
 Var obj := LpOpt(my_qp);
 For i := @constraint Do (
    WhatIf((LpOpt(my_qp), If @constraint = i Then rhs + delta else rhs) - obj)/delta

where my_qp is the variable defined by QpDefine, constraint is the constraint index passed to QpDefine in my_qp, and rhs is a variable passed as the «rhs» parameter to QpDefine. This causes the QCP to be solved multiple times to compute these shadow prices.

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