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Valid Inequalities for Separable Concave Constraints with Indicator Variables [chapter]

Cong Han Lim, Jeff Linderoth, James Luedtke
2016 Lecture Notes in Computer Science  
Abstract We study valid inequalities for optimization models that contain both binary indicator variables and separable concave constraints.  ...  Using this analysis, we demonstrate how valid inequalities for the single node flow set and for the lot-sizing polyhedron can be "tilted" to give valid inequalities that also account for separable concave  ...  ( , S) inequalities are not used. 123 Conclusion We study valid inequalities for a mixed-integer nonlinear set having binary indicator variables and separable concave constraints.  ... 
doi:10.1007/978-3-319-33461-5_23 fatcat:d3si5uzmmnd2jdco7onrxkrt24

On Valid Inequalities for Quadratic Programming with Continuous Variables and Binary Indicators [chapter]

Hongbo Dong, Jeff Linderoth
2013 Lecture Notes in Computer Science  
Finally, we show the separation problem for lifted-concave-QPB inequalities is tractable if the number of binary variables involved in the inequality is small.  ...  First, all lifted-concave-QPB inequalities define the relevant convex hull for the case of convex quadratic programming with indicators.  ...  Note that B • X + α T x + γ ≤ δ T z is a valid lifted-concave-QPB inequality and Card In the separation problem, we write constraints defining V |I| for variables I we want appearing in the lifted-concave-QPB  ... 
doi:10.1007/978-3-642-36694-9_15 fatcat:2nhrrm4l5fgj7ik6s4dkouzsiy

Bi-perspective functions for mixed-integer fractional programs with indicator variables

Adam N. Letchford, Qiang Ni, Zhaoyu Zhong
2020 Mathematical programming  
More recently, they have been used to form tight relaxations of mixedinteger nonlinear programs with so-called indicator variables.  ...  Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously.  ...  The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.  ... 
doi:10.1007/s10107-020-01519-9 fatcat:qelhlexfcbh6hg5hfigf2yirva

Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables [article]

Alper Atamturk, Hyemin Jeon
2018 arXiv   pre-print
The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints.  ...  We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization.  ...  Acknowledgement This research is supported, in part, by grant FA9550-10-1-0168 from the Office of the Assistant Secretary of Defense for Research and Engineering.  ... 
arXiv:1705.05915v3 fatcat:ql5o6ht27vb6jbivxh3h4rxhci

Intersection cuts for factorable MINLP [article]

Felipe Serrano
2018 arXiv   pre-print
We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain.  ...  Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.  ...  He would also like to thank Sven Wiese, Ambros Gleixner, Dan Steffy and Juan Pablo Vielma for helpful discussions, and Leon Eifler, Daniel Rehfeldt for comments that improved the manuscript.  ... 
arXiv:1812.03073v1 fatcat:6ef2sy4og5gd3jrkfdtkrm3tp4

Intersection Cuts for Factorable MINLP [chapter]

Felipe Serrano
2019 Lecture Notes in Computer Science  
We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain.  ...  Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.  ...  He would also like to thank Sven Wiese, Ambros Gleixner, Dan Steffy and Juan Pablo Vielma for helpful discussions, and Leon Eifler, Daniel Rehfeldt for comments that improved the manuscript.  ... 
doi:10.1007/978-3-030-17953-3_29 fatcat:xfpvmpuwtfdtnmqfxnbiaug7tm

Lifting convex inequalities for bipartite bilinear programs [article]

Xiaoyi Gu, Santanu S. Dey, Jean-Philippe P. Richard
2021 arXiv   pre-print
Using this subadditive approximation, we lift fixed variable pairs in closed-form, thus deriving a lifted bilinear cover inequality that is valid for general separable bipartite bilinear sets with box  ...  Our first main result shows that, for sets described by one bipartite bilinear constraint together with bounds, it is always possible to sequentially lift a seed inequality that is valid for a restriction  ...  To the best of our knowledge, this is the first study that derives lifted valid inequalities for general non-convex quadratic constraints with arbitrary number of variables.  ... 
arXiv:2106.12625v1 fatcat:qlsbxiqnxbe3fgsxgeryeaxdjy

Parametric Convex Quadratic Relaxation of the Quadratic Knapsac Problem [article]

Marcia Fampa, Daniela Cristina Lubke, Fei Wang, Henry Wolkowicz
2019 arXiv   pre-print
Finally, we propose new valid inequalities on the lifted matrix variable, derived from cover and knapsack inequalities for the QKP, and present the separation problems to generate cuts for the current  ...  Our best bounds are obtained from alternating between optimizing the parametric quadratic relaxation over the perturbation and adding cutting planes generated by the valid inequalities proposed.  ...  To improve the results, we also consider in our initial relaxation the valid inequalities obtained by multiplying the capacity constraint by each nonnegative variable x i , and also valid inequalities  ... 
arXiv:1901.06714v2 fatcat:jsa32emhtfditji5f754ufdmzu

New Outer Bounds on the Marginal Polytope

David A. Sontag, Tommi S. Jaakkola
2007 Neural Information Processing Systems  
When combined with a concave upper bound on the entropy, this gives a new variational inference algorithm for probabilistic inference in discrete Markov Random Fields (MRFs).  ...  Valid constraints on the marginal polytope are derived through a series of projections onto the cut polytope. As a result, we obtain tighter upper bounds on the log-partition function.  ...  Acknowledgments The authors thank Amir Globerson and David Karger for helpful discussions. This work was supported in part by the DARPA Transfer Learning program.  ... 
dblp:conf/nips/SontagJ07 fatcat:upjsglbrkzg4lgv6ek4hd62ucq

Maximizing a class of submodular utility functions

Shabbir Ahmed, Alper Atamtürk
2009 Mathematical programming  
However, the standard formulation of these problems using submodular inequalities is ineffective for their solution, except for very small instances.  ...  We show the lifting problem of the submodular inequalities to be a submodular maximization problem with a special structure solvable by a greedy algorithm, which leads to an easily-computable strengthening  ...  Acknowledgements The authors are thankful to the associate editor and a referee for their constructive comments.  ... 
doi:10.1007/s10107-009-0298-1 fatcat:kisqitzwm5h65l5v5keyc3m55y

Two-sided linear chance constraints and extensions [article]

Miles Lubin and Daniel Bienstock and Juan Pablo Vielma
2016 arXiv   pre-print
constraints of direct interest for applications in power systems.  ...  With a view towards practical computations, we develop a second-order cone outer approximation of the two-sided chance constraint with provably small approximation error.  ...  Acknowledgements We thank Michael (Misha) Chertkov of Los Alamos National Laboratory for discussions which inspired this work. M.  ... 
arXiv:1507.01995v2 fatcat:oecd5s7ivzagraw66mctb36dta

Reformulation and convex relaxation techniques for global optimization

Leo Liberti
2004 4OR  
This thesis is concerned with techniques for establishing such global optima using spatial Branch-and-Bound (sBB) algorithms.  ...  One notable exception is that of monomials of odd degree, i.e. expressions of the form , when the range of the variable includes zero.  ...  bilinear programs 60 3.1 3.4.1 Valid reduction constraints by multiplication with variable § . . . . . . 74 3.4.2 Valid reduction constraints by multiplication with variable ¡ . . . . .  ... 
doi:10.1007/s10288-004-0038-6 fatcat:h7ahszha7fbinnuj5zrpoa4jgm

Algorithms for separable convex optimization with linear ascending constraints

P T Akhil, Rajesh Sundaresan
2018 Sadhana (Bangalore)  
The paper considers the minimization of a separable convex function subject to linear ascending constraints.  ...  The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a separable convex function over the bases of a polymatroid with a certain  ...  Acknowledgements This work was supported by the Indo-French Centre for Promotion of Advanced Research under Project Number 5100-IT1.  ... 
doi:10.1007/s12046-018-0890-2 fatcat:pi4kksrgnjgk3k55h6jkmqek5i

Sequential Convex Restriction and its Applications in Robust Optimization [article]

Dongchan Lee, Konstantin Turitsyn, Jean-Jacques Slotine
2019 arXiv   pre-print
By bounding the nonlinearity with concave envelopes and using Brouwer's fixed point theorem, the sufficient condition is expressed in terms of closed-form convex inequality constraints.  ...  problems with nonlinear equality constraints.  ...  (Robust Feasibility for State-Uncertainty Separable Constraints) For a given explicit variable u, there exists an implicit variable x that satisfies constraints f (x, u, w) = 0 and h(x, u, w) ≤ 0 for all  ... 
arXiv:1909.01778v1 fatcat:i3f7ra54ajewnevago7rproyoa

Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks

Frauke Liers, Alexander Martin, Maximilian Merkert, Nick Mertens, Dennis Michaels
2021 Journal of Global Optimization  
Relaxations are commonly established by convex underestimators, where each constraint function is considered separately.  ...  We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem.  ...  We thank Robert Weismantel for many fruitful discussions on different ideas connected with simultaneous convexification, and the anonymous reviewers for their constructive comments on this paper.  ... 
doi:10.1007/s10898-020-00974-0 fatcat:srlajiyxwbh2jpmuhczmmrkwxa
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