A polyhedral branch-and-cut approach to global optimization

Tawarmalani, Mohit; Sahinidis, Nikolaos V.

doi:10.1007/s10107-005-0581-8

Cited by 1,071 publications

(655 citation statements)

References 16 publications

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“…Although αBB addresses the broader class of MINLP, it has specialized routines to handle MIQCQP via the convex envelopes of bilinear terms [11,91]. -BARON [26,133,134,135] Like αBB, the BARON code base addresses general MINLP to ε-global optimality but specializes its approach for MIQCQP. In addition to relaxing bilinear terms using the convex hull, the BARON preprocessing routines detect connected multivariable terms within quadratic equations [26].…”

Section: Literature Reviewmentioning

confidence: 99%

“…To test the performance of the solver GloMIQO, we compared the 399 test problems outlined in Table 2 against the state-of-the-art global optimization solvers listed in Table 1: BARON 10.1.2 [135], Couenne 0.4 [27], LindoGLOBAL 6.1.1.588 [63,87], and SCIP 2.1.0 [2,3,30,31]. Linus Schrage of LINDO Systems has generously given us a particularly highperforming version of LindoGLOBAL 6.1.1.588 [63,87]; the license permits us to input problems larger than the typical 2000 variable/3000 constraint limit in GAMS and allows us to access an undocumented quadratic mode option in LindoGLOBAL.…”

Section: Testing the Global Mixed-integer Quadratic Optimizer (Glomiqo)mentioning

confidence: 99%

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GloMIQO: Global mixed-integer quadratic optimizer

2012

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This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2,

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Section: Literature Reviewmentioning

confidence: 99%

Section: Testing the Global Mixed-integer Quadratic Optimizer (Glomiqo)mentioning

confidence: 99%

GloMIQO: Global mixed-integer quadratic optimizer

2012

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“…One of the most well-known solvers for MINLP problems is the BARON (Branch And Reduce Optimization Navigator) solver [23]. For a review of the available solvers, we refer the reader to [3].…”

Section: Introductionmentioning

confidence: 99%

Branch and Bound Based Coordinate Search Filter Algorithm for Nonsmooth Nonconvex Mixed-Integer Nonlinear Programming Problems

Fernandes

Costa

Fernandes

2014

Computational Science and Its Applications – ICCSA 2014

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Abstract. A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictions on some variables. When they are nonconvex then they are the most difficult to solve above all. We present a methodology to solve nonsmooth nonconvex MINLP problems based on a branch and bound paradigm and a stochastic strategy. To solve the relaxed subproblems at each node of the branch and bound tree search, an algorithm based on a multistart strategy with a coordinate search filter methodology is implemented. The produced numerical results show the robustness of the proposed methodology.

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“…Derivative-free versions of Algencan were introduced in [31] and [49]. There exist many global optimization techniques for nonlinear programming problems, e.g., [2,3,4,14,38,40,41,42,43,44,50,52,53,58,62,63,65,66,67,68,69,70,73,75]. The main appeal of the augmented Lagrangian approach in this context is that the structure of this method makes it possible to take advantage of global optimization algorithms for simpler problems, i.e.…”

Section: Introductionmentioning

confidence: 99%

Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming

2013

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In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the αBB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given.

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A polyhedral branch-and-cut approach to global optimization

Cited by 1,071 publications

References 16 publications

GloMIQO: Global mixed-integer quadratic optimizer

GloMIQO: Global mixed-integer quadratic optimizer

Branch and Bound Based Coordinate Search Filter Algorithm for Nonsmooth Nonconvex Mixed-Integer Nonlinear Programming Problems

Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming

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