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Global optimization of nonconvex problems with multilinear intermediates

Xiaowei Bao, Aida Khajavirad, Nikolaos V. Sahinidis, Mohit Tawarmalani
2014 Mathematical Programming Computation  
We consider global optimization of nonconvex problems containing multilinear functions.  ...  , multilinear problems, and polynomial optimization problems. 123 2 X.  ...  First, to demonstrate the key role of our decomposition algorithm in efficient solution of nonconvex problems with multilinear intermediates to global optimality.  ... 
doi:10.1007/s12532-014-0073-z fatcat:xni6phwtgjdszhjdbf72ox7fge

A Review of Deterministic Optimization Methods in Engineering and Management

Ming-Hua Lin, Jung-Fa Tsai, Chian-Son Yu
2012 Mathematical Problems in Engineering  
With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed.  ...  A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.  ...  However, optimization problems often include nonconvex functions that cannot be dealt with by the standard local optimization techniques to guarantee global optimality efficiently.  ... 
doi:10.1155/2012/756023 fatcat:axwcogt5tbhljkz3fh5d7hs6ti

A review of recent advances in global optimization

C. A. Floudas, C. E. Gounaris
2008 Journal of Global Optimization  
It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization  ...  This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006) (2007) (2008).  ...  Floudas gratefully acknowledges support from the National Science Foundation, the National Institutes of Health (R01 GM52032 and R24 GM069736), the Environmental Protection Agency (GAD R 832721-010), AspenTech  ... 
doi:10.1007/s10898-008-9332-8 fatcat:72fpfq72hrdzhf6mxqyc6ssezm

Relaxations of factorable functions with convex-transformable intermediates

Aida Khajavirad, Jeremy J. Michalek, Nikolaos V. Sahinidis
2012 Mathematical programming  
We propose to strengthen standard factorable relaxations of global optimization problems through the use of functional transformations of intermediate expressions.  ...  In particular, we exploit convex transformability of the component functions of factorable programs as a tool in the generation of bounds.  ...  Acknowledgments The authors would like to thank two anonymous referees for comments and suggestions that improved the quality of this manuscript.  ... 
doi:10.1007/s10107-012-0618-8 fatcat:3bkvvyx235c55lztw27r56psja

APOGEE: Global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes

Ruth Misener, Jeffrey P. Thompson, Christodoulos A. Floudas
2011 Computers and Chemical Engineering  
Our recent work globally optimized two classes of large-scale pooling problems: (i) a generalized pooling problem that treats the network topology as a decision variable [Misener and Floudas, 2010] and  ...  We have also unified our work by developing APOGEE (Algorithms for Pooling-problem global Optimization in GEneral and Extended classes), a computational tool that globally optimizes standard, generalized  ...  mixed-integer nonconvex program (nonconvex MINLP) with quadratic equalities and inequalities that exhibits multiple locally optimal solutions.  ... 
doi:10.1016/j.compchemeng.2011.01.026 fatcat:rq374pi47javfe4dwacwv64fri

Domain reduction techniques for global NLP and MINLP optimization

Yash Puranik, Nikolaos V. Sahinidis
2017 Constraints  
) optimization problems.  ...  We also present a computational analysis of the impact of these techniques on the performance of various widely available global solvers on a collection of 1740 test problems.  ...  Academic Press, New York (1992) [19] Bao, X., Khajavirad, A., Sahinidis, N.V., Tawarmalani, M.: Global optimization of nonconvex problems with multilinear intermediates.  ... 
doi:10.1007/s10601-016-9267-5 fatcat:drn6m456x5dhteazf4uem33bki

Accelerating Branch-and-Bound through a Modeling Language Construct for Relaxation-Specific Constraints

Nikolaos V. Sahinidis, Mohit Tawarmalani
2005 Journal of Global Optimization  
In the second application area, we communicate with the relaxation constructor the first-order optimality conditions for unconstrained global optimization problems.  ...  This approach is illustrated for the pooling problem and computational results show that it results in a scheme that makes global optimization nearly as fast as local optimization for pooling problems  ...  global optimization of nonconvex nonlinear and mixed-integer nonlinear programs.  ... 
doi:10.1007/s10898-004-2705-8 fatcat:fwpucjpqhvfejddhjljkws545q

Optimal DR-Submodular Maximization and Applications to Provable Mean Field Inference [article]

An Bian, Joachim M. Buhmann, Andreas Krause
2018 arXiv   pre-print
Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, can only generate local optima.  ...  It is a one-pass algorithm with linear time complexity, reaching the optimal 1/2 approximation ratio, which may be of independent interest.  ...  All of the mean field approximation problems investigated in this work fall into the following nonconvex maximization problem: maximize x∈[a, b] f (x), (P) where f : X → R is continuous DR-submodular,  ... 
arXiv:1805.07482v2 fatcat:piy54325tbchbbml3agtyr7zju

On decomposability of Multilinear sets

Alberto Del Pia, Aida Khajavirad
2017 Mathematical programming  
Such sets appear in factorable reformulations of many types of nonconvex optimization problems, including binary polynomial optimization.  ...  Finally, we propose a polynomial-time algorithm to optimally decompose a Multilinear set into simpler subsets.  ...  Factorable programming techniques are used widely in global optimization of mixed-integer nonlinear optimization problems (MINLPs) for bounding general nonconvex functions [20] .  ... 
doi:10.1007/s10107-017-1158-z fatcat:ded2prd7yjfxpfvoac5gffojmi

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Fani Boukouvala, Ruth Misener, Christodoulos A. Floudas
2016 European Journal of Operational Research  
Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems.  ...  This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO).  ...  Using deterministic global optimization of nonconvex MINLP to solve industriallyrelevant problems is not new; Floudas and Aggarwal (1990) , Visweswaran and Floudas (1990) , Floudas and Visweswaran (  ... 
doi:10.1016/j.ejor.2015.12.018 fatcat:jwe7b7ivrzhrjbttdl74eff2pe

Fast algorithms for Higher-order Singular Value Decomposition from incomplete data [article]

Yangyang Xu
2016 arXiv   pre-print
In this paper, we formulate an incomplete HOSVD problem and combine the two steps into solving a single optimization problem, which simultaneously achieves imputation of missing values and also tensor  ...  We also present two algorithms for solving the problem based on block coordinate update. Global convergence of both algorithms is shown under mild assumptions.  ...  Due to nonconvexity of (2.2), we cannot in general guarantee global optimality, so instead we aim at showing the first-order optimality conditions in (3.1) holds in the limit.  ... 
arXiv:1411.4324v2 fatcat:xipgenc5pjfj5dxyptfmsztnla

Fast Algorithms for Higher-Order Singular Value Decomposition from Incomplete Data

Yangyang Xu
2017 Journal of Computational Mathematics  
In this paper, we formulate an incomplete HOSVD problem and combine the two steps into solving a single optimization problem, which simultaneously achieves imputation of missing values and also tensor  ...  Global convergence of the algorithm is shown under mild assumptions and implies that of the popular higher-order orthogonality iteration (HOOI) method, and thus we, for the first time, give global convergence  ...  Due to nonconvexity of (2.2), we cannot in general guarantee global optimality, so instead we aim at showing the first-order optimality conditions in (3.1) hold in the limit.  ... 
doi:10.4208/jcm.1608-m2016-0641 fatcat:t3hawzcivjgrfg2qgmacsvpecm

ADMM for Multiaffine Constrained Optimization [article]

Wenbo Gao, Donald Goldfarb, Frank E. Curtis
2019 arXiv   pre-print
To illustrate the applicability of our results, we describe examples including nonnegative matrix factorization, sparse learning, risk parity portfolio selection, nonconvex formulations of convex problems  ...  Specifically, we show that ADMM, when employed to solve problems with multiaffine constraints that satisfy certain verifiable assumptions, converges to the set of constrained stationary points if the penalty  ...  Acknowledgements We thank Qing Qu, Yuqian Zhang, and John Wright for helpful discussions about applications of multiaffine ADMM.  ... 
arXiv:1802.09592v3 fatcat:pg4wdgfpdng4xo2qozwfrwl3ha

Generalized Face Super-Resolution

Kui Jia, Shaogang Gong
2008 IEEE Transactions on Image Processing  
Our experiments show not only performance superiority over existing benchmark face super-resolution techniques on single modal face hallucination, but also novelty of our approach in coping with multimodal  ...  of low-resolution face images as probe.  ...  (c) Intermediate face warping results in our iterative optimization of face alignment process [the optimization starts from (a)-I, and converges at (b)-I after ten iterations].  ... 
doi:10.1109/tip.2008.922421 pmid:18482883 fatcat:p4mjwtmtgngrjf23a27z6qt44i

Complete search in continuous global optimization and constraint satisfaction

Arnold Neumaier
2004 Acta Numerica  
This survey covers the state of the art of techniques for solving generalpurpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques  ...  After giving motivations for and important examples of applications of global optimization, a precise problem definition is given, and a general form of the traditional first-order necessary conditions  ...  This survey is part of work done in the context of the COCONUT project (COCONUT 2001) sponsored by the European Union, with the goal of integrating various existing complete approaches to global optimization  ... 
doi:10.1017/s0962492904000194 fatcat:phckdsbkevdahcawdroqwwgoeq
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