The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and nonnegative real edge distances d, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to optimality is … Read more
A Greedy Randomized Adaptive Search Procedure (GRASP) is an iterative multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications … Read more
We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. Using a Sample Average Approximation (SAA) approach … Read more
We propose a trust-region algorithm for constrained optimization problems in which the derivatives of the objective function are not available. In each iteration, the objective function is approximated by a model obtained by quadratic interpolation, which is then minimized within the intersection of the feasible set with the trust region. Since the constraints are handled … Read more
In this paper, we rigorously study tractable models for provably recovering low-rank tensors. Unlike their matrix-based predecessors, current convex approaches for recovering low-rank tensors based on incomplete (tensor completion) and/or grossly corrupted (tensor robust principal analysis) observations still suffer from the lack of theoretical guarantees, although they have been used in various recent applications and … Read more
In this paper, we consider the multi-band robust knapsack problem which generalizes the Γ-robust knapsack problem by subdividing the single deviation band into several smaller bands. We state a compact ILP formulation and develop two dynamic programming algorithms based on the presented model where the first has a complexity linear in the number of items … Read more
Within a nonzero, real Banach space we study the problem of characterising a maximal extension of a monotone operator in terms of minimality properties of representative functions that are bounded by the Penot and Fitzpatrick functions. We single out a property of this space of representative functions that enable a very compact treatment of maximality … Read more
We propose an algorithm for solving the surrogate dual of a mixed integer program. The algorithm uses a trust region method based on a piecewise affine model of the dual surrogate value function. A new and much more flexible way of updating bounds on the surrogate dual’s value is proposed, which numerical experiments prove to … Read more
This paper deals with the Close-Enough Traveling Salesman Problem (CETSP). In the CETSP, rather than visiting the vertex (customer) itself, the salesman must visit a specific region containing such vertex. To solve this problem, we propose a simple yet effective exact algorithm, based on Branch-and-Bound and Second Order Cone Programming (SOCP). The proposed algorithm was … Read more
Robust optimization is an important technique to immunize optimization problems against data uncertainty. In the case of a linear program and an ellipsoidal uncertainty set, the robust counterpart turns into a second-order cone program. In this work, we investigate the efficiency of linearizing the second-order cone constraints of the latter. This is done using the … Read more