1,734 research outputs found
Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs
This paper deals with uncertain multi-objective convex programming problems, where the data of the objective function or the constraints or both are allowed to be uncertain within specified uncertainty sets. We present sufficient conditions for the existence of highly robust weakly efficient solutions, that is, robust feasible solutions which are weakly efficient for any possible instance of the objective function within a specified uncertainty set. This is done by way of estimating the radius of highly robust weak efficiency under linearly distributed uncertainty of the objective functions. In the particular case of robust quadratic multi-objective programs, we show that these sufficient conditions can be expressed in terms of the original data of the problem, extending and improving the corresponding results in the literature for robust multi-objective linear programs under ball uncertainty.This research was partially supported by the Australian Research Council, Discovery Project DP120100467 and the MINECO of Spain and ERDF of EU, Grants MTM2014-59179-C2-1-P and ECO2016-77200-P
Notes on the value function approach to multiobjective bilevel optimization
This paper is concerned with the value function approach to multiobjective
bilevel optimization which exploits a lower level frontier-type mapping in
order to replace the hierarchical model of two interdependent multiobjective
optimization problems by a single-level multiobjective optimization problem. As
a starting point, different value-function-type reformulations are suggested
and their relations are discussed. Here, we focus on the situations where the
lower level problem is solved up to efficiency or weak efficiency, and an
intermediate solution concept is suggested as well. We study the
graph-closedness of the associated efficiency-type and frontier-type mappings.
These findings are then used for two purposes. First, we investigate existence
results in multiobjective bilevel optimization. Second, for the derivation of
necessary optimality conditions via the value function approach, it is inherent
to differentiate frontier-type mappings in a generalized way. Here, we are
concerned with the computation of upper coderivative estimates for the
frontier-type mapping associated with the setting where the lower level problem
is solved up to weak efficiency. We proceed in two ways, relying, on the one
hand, on a weak domination property and, on the other hand, on a scalarization
approach. Throughout the paper, illustrative examples visualize our findings,
the necessity of crucial assumptions, and some flaws in the related literature.Comment: 30 page
Metaheuristic design of feedforward neural networks: a review of two decades of research
Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era
Stochastic measures of financial markets efficiency and integration
The notion of integration of different fmancial markets is often related to the absence of crossmarket arbitrage
opportunities. Under the appropriated asswnptions and in absence of cross-market arbitrage opportunities, a riskneutral
probability measure, shared by both markets, must exist. Some authors have considered this to provide
some integration measures when the markets do not share any pricing rule, but always in static (or one period)
asset pricing models.
The purpose or this paper is to extend the refereed notions to a more general context. This is accomplished by
introducing a methodology which may be applied in any intertemporal dynamic asset pricing model and without
special asswnptions on the assets prices stochastic process. Then, the integration measures introduced here are
stochastic processes testing different relative arbitrage profits and depending on the state of nature and on the date.
The measures are introduced in a single fmancial market. When this market is not a global market from different
ones, the measures simply test the degree of market efficiency.
Transaction costs can be discounted in our model. Therefore, one can measure efficiency and integration in
models with frictions.
The main results are also interesting form a mathematical pint of view, since some topics of Operational Research
are involved. We provide a procedure to solve a vector optimization problem with a non differentiable objective
function and prove some properties about its sensitivity
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