Computing exact solution to nonlinear integer programming: Convergent Lagrangian and objective level cut method

Li, Duan; Wang, J.; Sun, Xiaoling

doi:10.1007/s10898-006-9128-7

Cited by 14 publications

(4 citation statements)

References 42 publications

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“…This is verified in other studies [21,19,16]. Strong duality in a form that allows practical, computationally useful methods to estimate bounds for IP has been elusive, although the recent work of Klabjan [27] and Li et al [31] offers great promise.…”

Section: Introductionsupporting

confidence: 57%

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On the augmented Lagrangian dual for integer programming

Boland

Eberhard

2014

Math. Program.

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We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pure integer programs.

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Section: Introductionsupporting

confidence: 57%

“…One surprising new development is the application of Z-transforms and complex variable techniques by Lasserre [28,29] to study the value function. Very recently, algorithms for solving the subadditive dual for both linear and nonlinear IP have been developed [27,31].…”

Section: Introductionmentioning

confidence: 99%

On the augmented Lagrangian dual for integer programming

Boland

Eberhard

2014

Math. Program.

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“…The algorithm OAC presented in this section differs from the algorithm OAA (Section 3.1) as follows: (i) it involves the construction of an inner approximation problem whose optimal solution provides an optimality cut, also called objective level cut [58,59], for the original problem (P2); (ii) the optimality cut is introduced in the formulation of the successive outer approximation problems.…”

Section: Outer Approximation Algorithm With Optimality Cut Oacmentioning

confidence: 99%

Construction of Risk-Averse Enhanced Index Funds

Lejeune

Samatlı-Paç

2010

SSRN Journal

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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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“…Furthermore, they proposed genetic algorithms with double strings using linear programming relaxation GADSLPR 16 for multiobjective multidimensional integer knapsack problems and genetic algorithms with double strings using linear programming relaxation based on reference solution updating GADSLPRRSU for linear integer programming problems 17 . Observing that some solution methods for specialized types of nonlinear integer programming problems have been proposed [18][19][20][21][22][23] , as an approximate solution method for general nonlinear integer programming problems, Sakawa et al 24 proposed genetic algorithms with double strings using continuous relaxation based on reference solution updating GADSCRRSU .…”

Section: Introductionmentioning

confidence: 99%

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Integer Programming Problems with Block-Angular Structures through Genetic Algorithms with Decomposition Procedures

Sakawa

Kato

2009

Advances in Operations Research

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We focus on multiobjective nonlinear integer programming problems with block-angular structures which are often seen as a mathematical model of large-scale discrete systems optimization. By considering the vague nature of the decision maker's judgments, fuzzy goals of the decision maker are introduced, and the problem is interpreted as maximizing an overall degree of satisfaction with the multiple fuzzy goals. For deriving a satisficing solution for the decision maker, we develop an interactive fuzzy satisficing method. Realizing the block-angular structures that can be exploited in solving problems, we also propose genetic algorithms with decomposition procedures. Illustrative numerical examples are provided to demonstrate the feasibility and efficiency of the proposed method.

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Computing exact solution to nonlinear integer programming: Convergent Lagrangian and objective level cut method

Cited by 14 publications

References 42 publications

On the augmented Lagrangian dual for integer programming

On the augmented Lagrangian dual for integer programming

Construction of Risk-Averse Enhanced Index Funds

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Integer Programming Problems with Block-Angular Structures through Genetic Algorithms with Decomposition Procedures

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