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作者：Fischetti, Matteo; Salvagnin, Domenico; Zanette, Arrigo
作者单位：University of Padua; University of Padua
摘要：A new cut selection criterion for Benders' cuts is proposed and computationally analyzed. The results show that the new criterion is more robust-and often considerably faster-than the standard ones.
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作者：Dukanovic, Igor; Rendl, Franz
作者单位：University of Maribor; University of Klagenfurt
摘要：The Lovasz theta number of a graph G can be viewed as a semidefinite programming relaxation of the stability number of G. It has recently been shown that a copositive strengthening of this semidefinite program in fact equals the stability number of G. We introduce a related strengthening of the Lovasz theta number toward the chromatic number of G, which is shown to be equal to the fractional chromatic number of G. Solving copositive programs is NP-hard. This motivates the study of tractable ap...
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作者：Liang, Dong; Wilhelm, Wilbert E.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：This paper proposes a generalization of column generation, reformulating the master problem with fewer variables at the expense of adding more constraints; the sub-problem structure does not change. It shows both analytically and computationally that the reformulation promotes faster convergence to an optimal solution in application to a linear program and to the relaxation of an integer program at each node in the branch-and-bound tree. Further, it shows that this reformulation subsumes and g...
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作者：Birgin, E. G.; Floudas, C. A.; Martinez, J. M.
作者单位：Universidade de Sao Paulo; Princeton University; Universidade Estadual de Campinas
摘要：A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.
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作者：Dentcheva, Darinka; Ruszczynski, Andrzej
作者单位：Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
摘要：We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconve...
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作者：Dutta, Joydeep; Pattanaik, Suvendu Ranjan; Thera, Michel
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur; Universite de Limoges; Centre National de la Recherche Scientifique (CNRS)
摘要：In this note we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the approximate multiplier rule.
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作者：Lodi, Andrea; Malaguti, Enrico; Stier-Moses, Nicolas E.
作者单位：University of Bologna; Columbia University
摘要：Inspired by the One Laptop Per Child project, we consider mesh networks that connect devices that cannot recharge their batteries easily. We study how the mesh should retransmit information to make use of the energy stored in each of the nodes effectively. The solution that minimizes the total energy spent by the whole network may be very unfair to some nodes because they bear a disproportionate burden of the traffic. A Nash equilibrium achieved when nodes minimize the energy they spend does n...
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作者：Iwata, Satoru; Takamatsu, Mizuyo
作者单位：University of Tokyo; Kyoto University
摘要：Modern modeling approaches for circuit analysis lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. The index of the DAE arising from the modified nodal analysis (MNA) is determined uniquely by the structure of the circuit. Instead, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant electric circuit...
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作者：Fernandez, Damian; Solodov, Mikhail
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the strong second-order sufficient condition for optimality (without any constraint qualification assumptions). We prove a stronger superlinear converge...
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作者：Dontchev, A. L.; Rockafellar, R. T.
作者单位：National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS); NSF - Division of Mathematical Sciences (DMS); University of Washington; University of Washington Seattle
摘要：In an extension of Newton's method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton's iterates as elements of a sequence space. An inverse function version of this result shows that the strong regularity of the mapping associated with the Newton sequences is equivalent to the strong regularity of the generalized equation m...
