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作者：Hanasusanto, Grani A.; Roitch, Vladimir; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
摘要：The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set chara...
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作者：Nie, Jiawang
作者单位：University of California System; University of California San Diego
摘要：Let be a finite subset of and be the space spanned by monomials with . Let be a compact semialgebraic set of such that a polynomial in is positive on . Denote by the cone of polynomials in that are nonnegative on . The dual cone of is , the set of all truncated moment sequences in that admit representing measures supported in . First, we study geometric properties of the cones and (like interiors, closeness, duality, memberships), and construct a convergent hierarchy of semidefinite relaxation...
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作者：Van Hentenryck, P.; Coffrin, C.
作者单位：NICTA; Australian National University
摘要：This paper studies the use of mathematical programming for the repair and restoration of a transmission system after a significant disruption (e.g., a natural disaster). Such blackouts may last several days and have significant impact on human and economic welfare. The transmission system repair and restoration problem (TSRRP) consists in dispatching crews to repair damaged electrical components in order to minimize the size of the blackout. The TSRRP can be modeled as a large-scale mixed nonl...
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作者：He, Qie; Ahmed, Shabbir; Nemhauser, George L.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University System of Georgia; Georgia Institute of Technology
摘要：The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when all sources are in the first echelon and all sinks are in two echelons, and when there is a single source but many sinks in multiple e...
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作者：Netzer, Tim; Sanyal, Raman
作者单位：Leipzig University; Free University of Berlin
摘要：Hyperbolicity cones are convex algebraic cones arising from hyperbolic polynomials. A well-understood subclass of hyperbolicity cones is that of spectrahedral cones and it is conjectured that every hyperbolicity cone is spectrahedral. In this paper we prove a weaker version of this conjecture by showing that every smooth hyperbolicity cone is the linear projection of a spectrahedral cone, that is, a spectrahedral shadow.
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作者：Burer, Samuel
作者单位：University of Iowa
摘要：This paper illustrates the fundamental connection between nonconvex quadratic optimization and copositive optimization-a connection that allows the reformulation of nonconvex quadratic problems as convex ones in a unified way. We focus on examples having just a few variables or a few constraints for which the quadratic problem can be formulated as a copositive-style problem, which itself can be recast in terms of linear, second-order-cone, and semidefinite optimization. A particular highlight ...
