An algorithm for separable piecewise convex programming problems
Richard M. Soland · Naval Research Logistics Quarterly · 1973
Abstract We present a branch and bound algorithm to solve mathematical programming problems of the form: Find x =|(x1,…xn) to minimize Σϕi0(x1) subject to xϵG, l≦x≦L and Σϕi0(x1)≦0, j=1,…,m. With l=(l1,…,ln) and L=(L1,…,Ln), each ϕij is assumed to be lower aemicontinuous and piecewise convex on the finite interval [li.Li]. G is assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems; these correspond to successive partitions of the set C={x|l ≦ x ≦L} on the bahis of the piecewise convexity of the problem functions ϕij. Computational considerations are discussed, and an illustrative example is presented.