We provide information on the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design that can be accessed at http://sndlib.zib.de. In version 1.0, the library contains data related to 22 networks which, combined with a set of selected planning parameters, leads to 830 network planning problem instances. In this paper, we … Read more
We generalize the Nelder-Mead simplex and LTMADS algorithms and, the frame based methods for function minimization to Riemannian manifolds. Examples are given for functions defined on the special orthogonal Lie group $\mathcal{SO}(n)$ and the Grassmann manifold $\mathcal{G}(n,k)$. Our main examples are applying the generalized LTMADS algorithm to equality constrained optimization problems and, to the Whitney … Read more
We present a general procedure for handling equality constraints in optimization problems that is of particular use in direct search methods. First we will provide the necessary background in differential geometry. In particular, we will see what a Riemannian manifold is, what a tangent space is, how to move over a manifold and how to … Read more
We extend direct search methods to optimization problems that include equality constraints given by Lipschitz functions. The equality constraints are assumed to implicitly define a Lipschitz manifold. Numerically implementing the inverse (implicit) function theorem allows us to define a new problem on the tangent spaces of the manifold. We can then use a direct search … Read more
A direct search method for the class of problems considered by Lewis and Torczon [\textit{SIAM J. Optim.}, 12 (2002), pp. 1075-1089] is developed. Instead of using an augmented Lagrangian method, a simplicial approximation method to the feasible set is implicitly employed. This allows the points our algorithm considers to conveniently remain within an \textit{a priori} … Read more
Operational risks are defined as risks of human origin. Unlike financial risks that can be handled in a financial manner (e.g. insurances, savings, derivatives), the treatment of operational risks calls for a “managerial approach”. Consequently, we propose a new way of dealing with operational risk, which relies on the well known aggregate planning model. To … Read more
We consider the problem of maximizing a nondecreasing submodular set function over various constraint structures. Specifically, we explore the performance of the greedy algorithm, and a related variant, the locally greedy algorithm in solving submodular function maximization problems. Most classic results on the greedy algorithm and its variant assume the existence of an optimal polynomial-time … Read more
This paper presents a three-stage optimization algorithm for solving two-stage robust decision making problems under uncertainty with min-max regret objective. The structure of the first stage problem is a general mixed integer (binary) linear programming model with a specific model of uncertainty that can occur in any of the parameters, and the second stage problem … Read more
In this work we develop a primal-dual short-step interior point method for conic convex optimization problems for which exact evaluation of the gradient and Hessian of the barrier function is either impossible or too expensive. As our main contribution, we show that if approximate gradients and Hessians can be computed, and the relative errors in … Read more
The minimum k-partition (MkP) problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in the same partition. The main contribution of this paper is the design and implementation of a branch-and-cut algorithm based on semidefinite … Read more