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We present new first and second-order optimality conditions for maximizing a function over a polyhedron. These conditions are expressed in terms of the first and second-order directional derivatives along the edges of the polyhedron, and an edge description of the polyhedron. If the objective function is quadratic and edge-convex, and the constraint(More)
The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper 10.1016/j.ejor.2014.05.042, the Vertex Separator Problem was formulated as a continuous (non-concave/non-convex) bilinear quadratic program. In this paper,(More)
Four NP-hard optimization problems on graphs are studied: The vertex separator problem, the edge separator problem, the maximum clique problem, and the maximum independent set problem. We show that the vertex separator problem is equivalent to a continuous bilinear quadratic program. This continuous formulation is compared to known continuous quadratic(More)
This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically(More)
Tetrodotoxin is a neurotoxin responsible for many human fatalities, most commonly following the consumption of pufferfish. Whilst the source of the toxin has not been conclusively proven, it is thought to be associated with various species of marine bacteria. Whilst the toxins are well studied in fish and gastropods, in recent years, there have been a(More)
Regular occurrence of brevetoxin-producing toxic phytoplankton in commercial shellfishery areas poses a significant risk to shellfish consumer health. Brevetoxins and their causative toxic phytoplankton are more limited in their global distribution than most marine toxins impacting commercial shellfisheries. On the other hand, trends in climate change could(More)
The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size. Recently, Hager and Hungerford [1] developed a continuous bilinear programming formulation of the VSP. In this paper, we reinforce the bilinear programming approach(More)
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