Results 11 to 20 of about 164,901 (283)
Integer convex minimization by mixed integer linear optimization [PDF]
Operations Research Letters, 2014 Minimizing a convex function over the integral points of a bounded convex set is polynomial in fixed dimension (Grötschel et al., 1988). We provide an alternative, short, and geometrically motivated proof of this result.
Oertel, Timm +2 more
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On the complexity of nonlinear mixed-integer optimization [PDF]
, 2010 This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained fully polynomial ...
Köppe, Matthias
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Polyhedral approximation in mixed-integer convex optimization [PDF]
Mathematical Programming, 2017 Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years.
Bent, Russell +3 more
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On the Complexity of Inverse Mixed Integer Linear Optimization [PDF]
SIAM Journal on Optimization, 2021 Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with the relationship of a particular inverse mixed integer linear optimization problem (MILP) to both the forward ...
Aykut Bulut, Ted K. Ralphs
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Information complexity of mixed-integer convex optimization
Mathematical Programming, 2023 We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) as the gap between the lower and upper bounds.
Amitabh Basu +3 more
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Disjunctive cuts in Mixed-Integer Conic Optimization
Mathematical Programming, 2022 This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization condition on its resolution. In particular, we show that a careful selection of normalization guarantees its solvability
Lodi A., Tanneau M., Vielma J. -P.
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A Mixed-Integer Optimization Formulation for Buyers Formation
Computers & Operations Research, 2023 Companies frequently offer wholesale prices for their products that decrease with the number of purchased items. However, single buyers may not be willing or able to purchase large quantities of a single item. Nevertheless, consumers can form groups to purchase at wholesale prices, obtaining bargaining power.
Dávila-Gálvez, Sebastián +4 more
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Mirror-Descent Methods in Mixed-Integer Convex Optimization [PDF]
, 2012 In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard.
A. Conn +15 more
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A Modified Jaya Algorithm for Mixed-Variable Optimization Problems
Journal of Intelligent Systems, 2018 Mixed-variable optimization problems consist of the continuous, integer, and discrete variables generally used in various engineering optimization problems.
Singh Prem, Chaudhary Himanshu
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Mathematics, 2022 This paper proposes a new solution methodology based on a mixed-integer conic formulation to locate and size photovoltaic (PV) generation units in AC distribution networks with a radial structure.
Oscar Danilo Montoya +2 more
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