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作者：O'Neill, Richard P.; Krall, Eric A.; Hedman, Kory W.; Oren, Shmuel S.
作者单位：Arizona State University; Arizona State University-Tempe; University of California System; University of California Berkeley
摘要：Currently, there is a need to plan and analyze the electric power transmission system in greater detail and over larger geographic areas. Existing models approach the problem from different perspectives. Each model addresses different aspects of and has different approximations to the optimal planning process. In order to scope out the huge challenge of optimal transmission planning, this paper presents a new modeling approach for inter-regional planning and investment in a competitive environ...
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作者：Kojima, Masakazu; Yamashita, Makoto
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：This paper is concerned with a class of ellipsoidal sets (ellipsoids and elliptic cylinders) in which are determined by a freely chosen m x m positive semidefinite matrix. All ellipsoidal sets in this class are similar to each other through a parallel transformation and a scaling around their centers by a constant factor. Based on the basic idea of lifting, we first present a conceptual min-max problem to determine an ellipsoidal set with the smallest size in this class which encloses a given ...
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作者：Burgdorf, Sabine; Cafuta, Kristijan; Klep, Igor; Povh, Janez
作者单位：University of Neuchatel; University of Ljubljana; University of Maribor; University of Ljubljana
摘要：The main topic addressed in this paper is trace-optimization of polynomials in noncommuting (nc) variables: given an nc polynomial f, what is the smallest trace can attain for a tuple of matrices ? A relaxation using semidefinite programming (SDP) based on sums of hermitian squares and commutators is proposed. While this relaxation is not always exact, it gives effectively computable bounds on the optima. To test for exactness, the solution of the dual SDP is investigated. If it satisfies a ce...
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作者：Candes, Emmanuel; Recht, Benjamin
作者单位：Stanford University; Stanford University; University of Wisconsin System; University of Wisconsin Madison
摘要：This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in can be efficiently recovered from 2s log n measurements with high probability and a rank r, n x n matrix can be efficiently recovered from r(6n - 5r) measurements with high probability. For sparse vectors, this is within an additive factor of the best known nonasymptotic bounds. For low-rank matrices, this matches ...
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作者：Pena, Javier; Roshchina, Vera
作者单位：Carnegie Mellon University; Federation University Australia; University of Evora
摘要：Consider a homogeneous multifold convex conic system Ax = 0, x is an element of K-1 x ... x K-r and its alternative system A(T) y is an element of K-1* x ... x K-r*, where K-1, ... , K-r are regular closed convex cones. We show that there is a canonical partition of the index set {1, ... , r} determined by certain complementarity sets associated to the most interior solutions to the two systems. Our results are inspired by and extend the Goldman-Tucker Theorem for linear programming.
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作者：Guigues, Vincent; Sagastizabal, Claudia
作者单位：Getulio Vargas Foundation; Universidade Federal do Rio de Janeiro
摘要：We consider risk-averse formulations of stochastic linear programs having a structure that is common in real-life applications. Specifically, the optimization problem corresponds to controlling over a certain horizon a system whose dynamics is given by a transition equation depending affinely on an interstage dependent stochastic process. We put in place a rolling-horizon time consistent policy. For each time step, a risk-averse problem with constraints that are deterministic for the current t...
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作者：Hoheisel, Tim; Kanzow, Christian; Schwartz, Alexandra
作者单位：University of Wurzburg
摘要：Mathematical programs with equilibrium constraints (MPECs) are difficult optimization problems whose feasible sets do not satisfy most of the standard constraint qualifications. Hence MPECs cause difficulties both from a theoretical and a numerical point of view. As a consequence, a number of MPEC-tailored solution methods have been suggested during the last decade which are known to converge under suitable assumptions. Among these MPEC-tailored solution schemes, the relaxation methods are cer...
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作者：Rodriguez-Chia, A. M.; Valero-Franco, C.
作者单位：Universidad de Cadiz
摘要：This paper presents a procedure to solve the classical location median problem where the distances are measured with l(p)-norms with p > 2. In order to do that we consider an approximated problem. The global convergence of the sequence generated by this iterative scheme is proved. Therefore, this paper closes the still open question of giving a modification of the Weiszfeld algorithm that converges to an optimal solution of the median problem with l(p) norms and p is an element of (2, infinity...
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作者：Eggermont, Christian E. J.; Schrijver, Alexander; Woeginger, Gerhard J.
作者单位：Eindhoven University of Technology; Centrum Wiskunde & Informatica (CWI); University of Amsterdam
摘要：We study algorithmic problems in multi-stage open shop processing systems that are centered around reachability and deadlock detection questions. We characterize safe and unsafe system states. We show that it is easy to recognize system states that can be reached from the initial state (where the system is empty), but that in general it is hard to decide whether one given system state is reachable from another given system state. We show that the problem of identifying reachable deadlock state...
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作者：Izmailov, Alexey F.; Kurennoy, Alexey S.; Solodov, Mikhail V.
作者单位：Lomonosov Moscow State University
摘要：We prove a new local upper Lipschitz stability result and the associated local error bound for solutions of parametric Karush-Kuhn-Tucker systems corresponding to variational problems with Lipschitzian base mappings and constraints possessing Lipschitzian derivatives, and without any constraint qualifications. This property is equivalent to the appropriately extended to this nonsmooth setting notion of noncriticality of the Lagrange multiplier associated to the primal solution, which is weaker...
