Solving mixed integer nonlinear programs by outer approximation

Fletcher, R.; Leyffer, Sven

doi:10.1007/bf01581153

Cited by 585 publications

(389 citation statements)

References 8 publications

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“…Algorithmic techniques used to solve MINLP problems are most often based on relaxation schemes. Solution approaches based on nonlinear branch-and-bound algorithms (see, e.g., [13,15,75]) or on outer approximations (see, e.g., [34,36,57,89]) have been proposed.…”

Section: Solution Methodsmentioning

confidence: 99%

Construction of Risk-Averse Enhanced Index Funds

Lejeune

Samatlı-Paç

2013

INFORMS Journal on Computing

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We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting the market risk exposure of the investors and the moral hazard associated with the wage structure of fund managers. The resulting stochastic integer problem is reformulated through the derivation of a deterministic equivalent for the risk constraint and the use of a block decomposition technique. We develop an exact outer approximation method based on the relaxation of some binary restrictions and the reformulation of the cardinality constraint. The method provides a hierarchical organization of the computations with expanding sets of integer-restricted variables and outperforms the Bonmin and the Cplex 12.1 solvers. The method can solve very large (up to 1000 securities) instances, converges fast, scales well, and is general enough to be applicable to problems with buy-in threshold constraints. Cross-validation tests show that the constructed funds track closely and are consistently less risky than the benchmark on the out-of-sample period.

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Section: Solution Methodsmentioning

confidence: 99%

Construction of Risk-Averse Enhanced Index Funds

Lejeune

Samatlı-Paç

2013

INFORMS Journal on Computing

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“…The tests are embedded within an outer approximation framework (Duran and Grossmann, 1986;Fletcher and Leyffer, 1994). To account for linearizations that are not strict underestimators of the nonconvex feasible space, global convexity tests (Kravanja and Grossmann, 1994) have been implemented.…”

Section: Proposed Algorithmmentioning

confidence: 99%

A feasibility-based algorithm for Computer Aided Molecular and Process Design of solvent-based separation systems

Gopinath

Galindo

Jackson

et al. 2016

Computer Aided Chemical Engineering

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“…The rationale for deriving a new solution framework comes from the observation of Kress et al that their enumerative algorithm is outperformed by the state-of-the-art MIP solver CPLEX for problems of moderate to large size. The key feature of the proposed solution framework is that it is based on an outer approximation (Duran and Grossmann, 1986;Fletcher and Leyffer, 1994) algorithm, which is enhanced by a new family of valid inequalities, a fixing strategy, and a new preprocessing method that groups possible realizations of the random vector in bundles defining identical requirements. The proposed methods constitute an efficient alternative to the sometimes computationally intensive enumerative methods for generating pLEPs, the cardinality of which is finite yet unknown.…”

Section: -(4)mentioning

confidence: 99%

Mathematical programming approaches for generating p-efficient points

Lejeune¹,

Noyan²

2010

European Journal of Operational Research

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Probabilistically constrained problems, in which the random variables are finitely distributed, are nonconvex in general and hard to solve. The p-efficiency concept has been widely used to develop efficient methods to solve such problems. Those methods require the generation of p-efficient points (pLEPs) and use an enumeration scheme to identify pLEPs. In this paper, we consider a random vector characterized by a finite set of scenarios and generate pLEPs by solving a mixed-integer programming (MIP) problem. We solve this computationally challenging MIP problem with a new mathematical programming framework. It involves solving a series of increasingly tighter outer approximations and employs, as algorithmic techniques, a bundle preprocessing method, strengthening valid inequalities, and a fixing strategy. The method is exact (resp., heuristic) and ensures the generation of pLEPs (resp., quasi pLEPs) if the fixing strategy is not (resp., is) employed, and it can be used to generate multiple pLEPs. To the best of our knowledge, generating a set of pLEPs using an optimization-based approach and developing effective methods for the application of the p-efficiency concept to the random variables described by a finite set of scenarios are novel. We present extensive numerical results that highlight the computational efficiency and effectiveness of the overall framework and of each of the specific algorithmic techniques.

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Solving mixed integer nonlinear programs by outer approximation

Cited by 585 publications

References 8 publications

Construction of Risk-Averse Enhanced Index Funds

Construction of Risk-Averse Enhanced Index Funds

A feasibility-based algorithm for Computer Aided Molecular and Process Design of solvent-based separation systems

Mathematical programming approaches for generating p-efficient points

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