Chvatal (1980) has given a simple example of a knapsack problem for which a branch-and-bound algorithm using domination and linear relaxations to eliminate subproblems will use an exponential number of steps in the best case. In this short note it is shown that Chvatals result remains true when the LP relaxation is replaced with a … Read more
A new branch-and-bound based algorithm for smooth nonconvex multiobjective optimization problems with convex constraints is presented. The algorithm computes an $(\varepsilon,\delta)$-approximation of all globally optimal solutions. We introduce the algorithm which uses selection rules, discarding and termination tests. The discarding tests are the most important aspect, as they examine in different ways whether a box … Read more
A symmetric matrix is called copositive if it generates a quadratic form taking no negative values over the nonnegative orthant, and the linear optimization problem over the set of copositive matrices is called the copositive programming problem. Recently, many studies have been done on the copositive programming problem (see, for example, \cite{aDUR10, aBOMZE12}). Among others, … Read more