Invited Session Fri.2.H 3003A

Friday, 13:15 - 14:45 h, Room: H 3003A

Cluster 6: Derivative-free & simulation-based optimization [...]

Multiple objectives in derivative-free optimization


Chair: Stefan Wild and Luís Nunes Vicente



Friday, 13:15 - 13:40 h, Room: H 3003A, Talk 1

Ana Luisa Custodio
Direct MultiSearch: A robust and efficient approach to multiobjective derivative-free optimization

Coauthors: Jose Aguilar Madeira, A. Ismael F. Vaz, Luís Nunes Vicente


In practical applications it is common to have several conflicting objective functions to optimize. Frequently, these functions exhibit nondifferentiabilities, are subject to numerical noise or are of black-box type, requiring the use of derivative-free optimization techniques.
In 2011 we proposed a multiobjective derivative-free methodology, called Direct Multisearch (DMS), suited for this type of applications, which generalizes to multiobjective optimization all direct-search methods of directional type. DMS is based on the search/poll framework, but uses the concept of Pareto dominance to maintain a list of nondominated points and to define a successful iteration.
Under the common assumptions used in direct-search for single objective optimization, and without considering any aggregation function for the several objectives involved in the problem definition, we proved that at least one limit point of the sequence of iterates generated by DMS lies in (a stationary form of) the Pareto front. Extensive computational experience has shown, however, that DMS has an impressive capability of generating the whole Pareto front.



Friday, 13:45 - 14:10 h, Room: H 3003A, Talk 2

Luís Nunes Vicente
Efficient cardinality/mean-variance portfolios

Coauthor: Rui Pedro Brito


We propose a novel approach to handle cardinality in portfolio
selection, by means of a biobjective cardinality/mean-variance
problem, allowing the investor to analyze the efficient tradeoff between return-risk and number of active positions.
Recent progress in multiobjective optimization without derivatives allow us to robustly compute (in-sample) the whole cardinality/mean-variance efficient frontier, for a variety of data sets and mean-variance models.
Our results show that a significant number of efficient
cardinality/mean-variance portfolios can overcome (out-of-sample) the naive strategy, while keeping transaction costs relatively low.



Friday, 14:15 - 14:40 h, Room: H 3003A, Talk 3

Francesco Rinaldi
Using an exact penalty function for multiobjective Lipschitz programs

Coauthors: Giovanni Fasano, Giampaolo Liuzzi, Stefano Lucidi


This work focuses on the solution of a constrained multiobjective optimization problem, with both nonlinear inequality constraints and bound constraints. We assume that the vector of the objective functions and the constraints are Lipschitz continuous. We issue the equivalence between the original constrained multiobjective problem, and a multiobjective problem with simple bounds, by means of an exact penalty function approach. We study the Pareto-Clarke stationary points of the multiobjective problem with bound constraints, and state their correspondence with the Pareto-Clarke stationary points of the original constrained multiobjective problem. We propose a line search based derivative free framework to issue the latter correspondence. We also report some numerical results proving the effectiveness of the proposed approach.


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