An effective logarithmic formulation for piecewise linearization requiring no inequality constraint

One of the commonly used techniques for tackling the nonconvex optimization problems in which all the nonlinear terms are univariate is the piecewise linear approximation by which the nonlinear terms are reformulated. The performance of the linearization technique primarily depends on the quantities of variables and constraints required in the formulation of a piecewise linear function. The state-of-the-art linearization method introduces $$2\lceil \log _2 m\rceil$$ 2 ⌈ log 2 m ⌉ inequality constraints, where m is the number of line segments in the constructed piecewise linear function. This study proposes an effective alternative logarithmic scheme by which no inequality constraint is incurred. The price that more continuous variables are needed in the proposed scheme than in the state-of-the-art method is less than offset by the simultaneous inclusion of a system of equality constraints satisfying the canonical form and the absence of any inequality constraint. Our numerical experiments demonstrate that the developed scheme has the computational superiority, the degree of which increases with m.