User guide · 2.0 development

Understanding solver results

Feasible solutions and bounds

A primal solution assigns values to the variables while satisfying the constraints and integrality requirements within tolerances. For minimization, its objective gives an upper bound on the optimum. A valid dual bound is a lower bound. For maximization, the directions reverse.

The gap measures the distance between these bounds. A small gap is useful only together with the feasibility and optimality tolerances and the solver’s reported status. Reaching a time or iteration limit does not establish optimality.

Outer approximation

SHOT constructs linear approximations of nonlinear expressions and solves mixed-integer subproblems. Primal searches seek feasible solutions to the original nonlinear problem. Convexity determines when linearizations provide globally valid bounds; nonconvex models require additional care and do not generally have the same guarantees.

Solver backends

The available MIP/NLP backends depend on compilation options and installed licenses. Select a backend available in your build and consult the settings reference. See the compilation guide for dependencies and the debugging guide for intermediate problems and diagnostic logs.