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Journal of Optimization Theory and Applications, 1988
We point out in this note that the class of cones in a locally convex topological vector space satisfying property (\(\Pi)\) or piecewise relatively weakly compact cones is exactly the class of cones admitting weakly compact bases or the class of cones whose closures admit weakly compact bases.
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We point out in this note that the class of cones in a locally convex topological vector space satisfying property (\(\Pi)\) or piecewise relatively weakly compact cones is exactly the class of cones admitting weakly compact bases or the class of cones whose closures admit weakly compact bases.
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1993
A cone C in R n is a set of points such that if x∈ C, then so is every nonnegative scalar multiple of x, i.e., if x∈C, then λx∈C for 0 ≤ λ∈R, x∈R n (see Figure 4.1.a for C in R2). If we consider the set of points X = {x}, then the cone generated by X is C = {y|y = λx, 0 ≤ λ∈ R, x∈X}. And if 0∉ X and for each y(≠0)∈C there are unique x∈X with λ > 0 such
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A cone C in R n is a set of points such that if x∈ C, then so is every nonnegative scalar multiple of x, i.e., if x∈C, then λx∈C for 0 ≤ λ∈R, x∈R n (see Figure 4.1.a for C in R2). If we consider the set of points X = {x}, then the cone generated by X is C = {y|y = λx, 0 ≤ λ∈ R, x∈X}. And if 0∉ X and for each y(≠0)∈C there are unique x∈X with λ > 0 such
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Motion planning around obstacles with convex optimization
Science Robotics, 2023Tobia Marcucci
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Curves ahead: molecular receptors for fullerenes based on concave–convex complementarity
Chemical Society Reviews, 2008Emilio M Pérez
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