Convex programming with single separable constraint and bounded variables

In this paper a minimization problem with convex objective function subject to a separable convex inequality constraint ‘⩽’ and bounded variables (box constraints) is considered. We propose an iterative algorithm for solving this problem based on line search and convergence of this algorithm is proved. At each iteration, a separable convex programming problem with the same constraint set is solved using Karush–Kuhn–Tucker conditions. Convex minimization problems subject to linear equality/ linear inequality ‘⩾’ constraint and bounds on the variables are also considered. Numerical illustration is included in support of theory.