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Tawarmalani, Mohit; Sahinidis, Nikolaos V.

doi:10.1023/a:1011233805045

Cited by 98 publications

(4 citation statements)

References 21 publications

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“…Tawarmalani & Sahinidis [29] introduce a method for the computation of convex and concave envelopes for the term ax by cx dy with x, y R 0 and a, b, c, d 0. By applying the exact same method, it is possible to derive convex and concave envelopes for the expression a1x a2x n i 1 biyi with x, y i R 0 and a 1 , a 2 , b i 0 for all i 1, .…”

Section: Sumdivmentioning

confidence: 99%

“…Envelopes for elementary univariate functions such as, e.g., exp, log, or x a , the binary product [18], and division [10,29] are already well-known in DGO. In order to improve convergence and computational time of the methods, envelopes have been developed for specific intrinsic functions such as, e.g., the trilinear product [30,31] or the function f x y 2 where f is known to be non-negative, concave, and relaxations and range bounds have to be calculated beforehand.…”

Section: Introductionmentioning

confidence: 99%

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Relaxations of thermodynamic property and costing models in process engineering

Najman

Bongartz

Mitsos

2019

Computers & Chemical Engineering

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Section: Sumdivmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relaxations of thermodynamic property and costing models in process engineering

Najman

Bongartz

Mitsos

2019

Computers & Chemical Engineering

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“…A description of the convex envelope was obtained explicitly for several specific classes of functions, e.g. for multilinear functions [23], for fractional terms [28] or for odd monomials [15]. Further results handle functions with specific curvature properties such as edge-convexity/concavity and indefiniteness [10,12,17,21].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integer nonlinear problems that uses simultaneous convexification. 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. In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations.

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“…Hence, in order to improve the efficiency in the solution of this kind of problems, the quadratic objective function of this problem will be approximated by a polyhedral outer approximation by means of perspective cuts (PC) as was suggested by Frangioni and Gentile (2006), so that we can exploit the efficiency of general-purpose solvers for mixed integer linear problems (MILP); in this case we use CPLEX 12.1. An alternative to the perspective cuts methodology is the Second-Order Cone Program reformulation (SOCP, Tawarmalani and Sahinidis (2001)), but for quadratic problems the perspective cuts reformulation was reported to be more efficient (Frangioni and Gentile (2009)). Finally, Branch-and-Fix Coordination (BFC) methods has also been used successfully to solve two-stage stochastic mixed integer linear problems (Escudero et al (2009)).…”

Section: Introductionmentioning

confidence: 99%

A new optimal electricity market bid model solved through perspective cuts

Corchero

Mijangos

Heredia

2011

TOP

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On current electricity markets the electrical utilities are faced with very sophisticated decision making problems under uncertainty. Moreover, when focusing in the short-term management, generation companies must include some medium-term products that directly influence their short-term strategies. In this work, the bilateral and physical futures contracts are included into the day-ahead market bid following MIBEL rules and a stochastic quadratic mixed-integer programming model is presented. The complexity of this stochastic programming problem makes unpractical the resolution of large-scale instances with general-purpose optimization codes. Therefore, in order to gain efficiency, a polyhedral outer approximation of the quadratic objective function obtained by means of perspective cuts (PC) is proposed. A set of instances of the problem has been defined with real data and solved with the PC methodology. The numerical results obtained show the efficiency of this methodology compared with standard mixed quadratic optimization solvers.Peer ReviewedPostprint (published version

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Untitled

Cited by 98 publications

References 21 publications

Relaxations of thermodynamic property and costing models in process engineering

Relaxations of thermodynamic property and costing models in process engineering

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

A new optimal electricity market bid model solved through perspective cuts

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