2010 **Abstract:** In classic optimization theory, the concept of stability refers to the study of how much and in which way the optimal solutions of a given minimization problem Π can vary as a function of small perturbations of the input data. Motivated by congestion problems arising in shortest-path based communication networks, in this paper we restrict ourselves to the case in which Π is actually a network design problem on a given graph G = (V,E,w) of |V| = n nodes, |E| = m edges, and with a positive real weight w(e) on ea…

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“…This adaptation enables us to at least generate a feasible solution in all cases, while for robust optimization in general, feasibility cannot be guaranteed. Optimization for stable inputs attempts to understand when and how small changes in the input data affect the solution [8,9,10,11,12,13]. Regret minimization and online learning focuses on finding a good solution in an online setting, revealing one input after another, assuming an arbitrary adversary [14].…”

confidence: 99%

“…This adaptation enables us to at least generate a feasible solution in all cases, while for robust optimization in general, feasibility cannot be guaranteed. Optimization for stable inputs attempts to understand when and how small changes in the input data affect the solution [8,9,10,11,12,13]. Regret minimization and online learning focuses on finding a good solution in an online setting, revealing one input after another, assuming an arbitrary adversary [14].…”

confidence: 99%

“…λ: An edge perturbation vector λ = λη m η=1 of λ-perturbation degree, i.e., λ ≤ λη ≤ 1, η = 1, • • • , m (Bilò et al, 2010). The definition is modified according to the strongest path problem of this work in contrast to the shortest path problem in (Bilò et al, 2010).…”

confidence: 99%

“…λ: An edge perturbation vector λ = λη m η=1 of λ-perturbation degree, i.e., λ ≤ λη ≤ 1, η = 1, • • • , m (Bilò et al, 2010). The definition is modified according to the strongest path problem of this work in contrast to the shortest path problem in (Bilò et al, 2010). The associated perturbed graph Gλ = G(V, E, wλ) is defined by multiplying the weights of the original G(V, E, w) by their associated perturbation value from λ.…”

confidence: 99%