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作者：Wolsey, Laurence A.; Yaman, Hande
作者单位：Universite Catholique Louvain; Ihsan Dogramaci Bilkent University
摘要：We study two continuous knapsack sets and with integer, one unbounded continuous and bounded continuous variables in either or form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of the bound constraints and polyhedra arising as the convex hulls of continuous knapsack sets with a single unbounded continuous variable. The latter convex hulls are completely described by an exponential family of partition i...
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作者：Cacchiani, Valentina; Juenger, Michael; Liers, Frauke; Lodi, Andrea; Schmidt, Daniel R.
作者单位：University of Bologna; University of Cologne; University of Erlangen Nuremberg; Universite de Montreal; Polytechnique Montreal
摘要：We study a single-commodity robust network design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of scenarios or as a polytope. We propose a branch-and-cut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming...
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作者：Carrizo, Gabriel A.; Lotito, Pablo A.; Maciel, Maria C.
作者单位：National University of the South; Instituto de Investigaciones en Ingenieria Electrica (IIIE); Comision Nacional de Energia Atomica (CNEA)
摘要：A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602-626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is int...
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作者：Kucukyavuz, Simge; Noyan, Nilay
作者单位：University System of Ohio; Ohio State University; Sabanci University
摘要：We consider a class of stochastic optimization problems that features benchmarking preference relations among random vectors representing multiple random performance measures (criteria) of interest. Given a benchmark random performance vector, preference relations are incorporated into the model as constraints, which require the decision-based random vector to be preferred to the benchmark according to a relation based on multivariate conditional value-at-risk (CVaR) or second-order stochastic...
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作者：Baes, Michel; Oertel, Timm; Weismantel, Robert
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard Karush-Kuhn-Tucker conditions involve separating hyperplanes, our extension is based on mixed-integer-free polyhedra. Our optimality conditions allow us to define an exact dual of our original mixed-integer convex problem.
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作者：Condat, Laurent
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or an -norm ball. It can be viewed as a Gauss-Seidel-like variant of Michelot's variable fixing algorithm; that is, the threshold used to fix the variables is updated after each element is read, instead of waiting for a full reading pass over the list of non-fixed elements. This algorithm is empirically demonstrated to be faster than existing methods.
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作者：Shtern, Shimrit; Ben-Tal, Aharon
作者单位：Technion Israel Institute of Technology; Tilburg University; Columbia University
摘要：Tracking problems are prevalent in the present day GPS and video systems. The problem of target tracking is a specific case of dynamic linear system estimation with additive noise. The most widely used filter for these systems is the Kalman filter (KF). The optimality of the KF and similar Bayesian filters is guaranteed under particular probabilistic assumptions. However, in practice, and specifically in applications such as tracking, these probabilistic assumptions are not realistic; indeed, ...
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作者：Kogan, Alexander; Lejeune, Miguel A.; Luedtke, James
作者单位：Rutgers University System; Rutgers University Newark; Rutgers University New Brunswick; George Washington University; University of Wisconsin System; University of Wisconsin Madison
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作者：Aronna, M. S.; Bonnans, J. F.; Goh, B. S.
作者单位：Getulio Vargas Foundation; Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Curtin University Malaysia
摘要：In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.
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作者：Dobre, Cristian; Duer, Mirjam; Frerick, Leonhard; Vallentin, Frank
作者单位：Wageningen University & Research; Universitat Trier; University of Cologne
摘要：In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the optimal solution of some infinite-dimensional copositive program. For this we develop a duality theory between the primal convex cone of copositive kernels and the dual convex cone of completely posit...
