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作者：Slot, Lucas; Laurent, Monique
作者单位：Centrum Wiskunde & Informatica (CWI); Tilburg University
摘要：We consider a hierarchy of upper approximations for the minimization of a polynomial f over a compact set K subset of R-n proposed recently by Lasserre (arXiv:1907.097784, 2019). This hierarchy relies on using the push-forward measure of the Lebesgue measure on K by the polynomial f and involves univariate sums of squares of polynomials with growing degrees 2r. Hence it is weaker, but cheaper to compute, than an earlier hierarchy by Lasserre (SIAM Journal on Optimization 21(3), 864-885, 2011),...
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作者：Gnegel, Fabian; Fuegenschuh, Armin; Hagel, Michael; Leyffer, Sven; Stiemer, Marcus
作者单位：Brandenburg University of Technology Cottbus; United States Department of Energy (DOE); Argonne National Laboratory
摘要：We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variab...
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作者：Anstreicher, Kurt M.; Burer, Samuel
作者单位：University of Iowa
摘要：We consider quadratic optimization in variables (x, y) where 0 <= x <= y, and y is an element of {0, 1}(n). Such binary variables are commonly referred to as indicator or switching variables and occur commonly in applications. One approach to such problems is based on representing or approximating the convex hull of the set {(x, xx(T,) yy(T)) : 0 <= x <= y is an element of{0, 1}(n)}. A representation for the case n = 1 is known and has been widely used. We give an exact representation for the ...
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作者：Kirches, Christian; Manns, Paul; Ulbrich, Stefan
作者单位：Braunschweig University of Technology; Technical University of Darmstadt
摘要：The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such th...
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作者：Liberti, Leo; Sager, Sebastian; Wiegele, Angelika
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Otto von Guericke University; University of Klagenfurt
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作者：Goettlich, Simone; Hante, Falk M.; Potschka, Andreas; Schewe, Lars
作者单位：University of Mannheim; Humboldt University of Berlin; TU Clausthal; University of Edinburgh
摘要：We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear ...
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作者：Chen, Zhongzhu; Fampa, Marcia; Lambert, Amelie; Lee, Jon
作者单位：University of Michigan System; University of Michigan; Universidade Federal do Rio de Janeiro; heSam Universite; Conservatoire National Arts & Metiers (CNAM)
摘要：The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-s principal submatrix of an order-n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for mixing these bounds to achieve better bounds.
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作者：Kleinert, Thomas; Grimm, Veronika; Schmidt, Martin
作者单位：University of Erlangen Nuremberg; University of Erlangen Nuremberg; University of Erlangen Nuremberg; Universitat Trier
摘要：Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel problems and the most recent algorithms use branch-and-cut techniques from mixed-integer programming that are especially tailored for the bilevel context. In this paper, we consider MIQP-QP bilevel problems, i.e., models with a mixed-integer convex-quadratic upper level and a continu...
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作者：Bestehorn, Felix; Hansknecht, Christoph; Kirches, Christian; Manns, Paul
作者单位：Braunschweig University of Technology
摘要：We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the rounding turns out to be difficult in the presence of switching costs or switching constraints as the underly...
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作者：Berthold, Timo; Csizmadia, Zsolt
摘要：It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and solution quality. It emphasizes the early part of the solution process by using an exponential decay. Thereby, it avoids that the order of solvers can be inverted by ...
