One of the commonly used techniques for tackling nonconvex optimization problems in which all nonlinear terms are univariate is piecewise linear approximation by reformulated. The performance linearization technique primarily depends on quantities variables and constraints required formulation a function. state-of-the-art method introduces $$2\lceil \log _2 m\rceil$$ inequality constraints, whe...

In this paper, we mainly study error bounds for a single convex inequality and semi-infinite constraint systems, give characterizations of stability via directional derivatives. For inequality, it is proved that the local under small perturbations essentially equivalent to non-zero minimum derivative at reference point over unit sphere, global be strictly positive infimum derivatives, all point...

For an inequality system defined by an infinite family of proper convex functions, we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions and study relationships between these new constraint qualifications and other wellknown constraint qualifications including the basic constraint qualification studied by Hiriart-Urrutty and Le...

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...