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We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1 + by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of… (More)

- Kwong Meng Teo, Dimitris J Bertsimas, D Healy, A Levi, P Seliger, Margret Bjarnadottir +16 others
- 2007

We propose a novel robust optimization technique, which is applicable to nonconvex and simulation-based problems. Robust optimization finds decisions with the best worst-case performance under uncertainty. If constraints are present, decisions should also be feasible under perturbations. In the real-world, many problems are noncon-vex and involve… (More)

- Dan Stratila
- 2012

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge… (More)

In this paper we study the dynamic version of the nonlinear minimum-cost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on edges that depend on time and flow. Moreover, we assume that the demand function and capacities of edges also depend on time. To solve the problem we propose an algorithm, which is… (More)

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge… (More)

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1 + by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of… (More)

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1 + by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of… (More)

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge… (More)

- Michel X. Goemans, Dan Stratila, ‖f∆− f∆v
- 2006

Lecture 10 We first provide a clarification of the discussion in Lectures 8 and 9 for the case of weighted graphs, and then discuss the sparsest cut problem and negative type metrics. Recall that in the previous lectures we considered a planar graph metric (X, d) and, for any ∆, gave an embedding f ∆ : X → ℓ 2 such that ∆ 32 ≤ f ∆ (u) − f ∆ (v) ≤ d(u, v),… (More)

- Santosh Vempala, Dan Stratila, Colin de Verdière
- 2005

Loosely speaking, an embedding of a graph G in R r consists of an injective mapping ψ : V → R r , and a correspondence from each edge ij ∈ E to a simple curve in R r with endpoints ψ(i) and ψ(j). Here a curve can be taken to be the image of a continuous injective function φ : [0, 1] → R r. An embedding in S 2 is defined similarly. In a planar embedding… (More)