A concave optimization-based approach for sparse multiobjective programming

Cocchi, Guido; Levato, Tommaso; Liuzzi, Giampaolo; Sciandrone, Marco

doi:10.1007/s11590-019-01506-w

Cited by 3 publications

(1 citation statement)

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“…We also included three datasets from the Fama/French benchmark collection (FF10, FF17, and FF48, with n equal to 10, 17, and 48), using the monthly returns from 07/1971 to 06/2011. The datasets are generated as in [42]. For each dataset, we define an instance of problem (6.1): the values of s and ν are set as reported in Table 3, and are such that the cardinality constraint is active at the optimal solution.…”

Section: Sparsity Constrained Optimization Problemsmentioning

confidence: 99%

Inexact penalty decomposition methods for optimization problems with geometric constraints

Kanzow

Lapucci

2023

Comput Optim Appl

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This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints are nonconvex and complicated, like cardinality constraints, disjunctive programs, or matrix problems involving rank constraints. By a variable duplication and decomposition strategy, the method presented here explicitly handles these difficult constraints, thus generating iterates which are feasible with respect to them, while the remaining (standard and supposingly simple) constraints are tackled by sequential penalization. Inexact optimization steps are proven sufficient for the resulting algorithm to work, so that it is employable even with difficult objective functions. The current work is therefore a significant generalization of existing papers on penalty decomposition methods. On the other hand, it is related to some recent publications which use an augmented Lagrangian idea to solve optimization problems with geometric constraints. Compared to these methods, the decomposition idea is shown to be numerically superior since it allows much more freedom in the choice of the subproblem solver, and since the number of certain (possibly expensive) projection steps is significantly less. Extensive numerical results on several highly complicated classes of optimization problems in vector and matrix spaces indicate that the current method is indeed very efficient to solve these problems.

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Section: Sparsity Constrained Optimization Problemsmentioning

confidence: 99%