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We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide  Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions  under the asymptotic convexity assumption.

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Scale deposits can reduce equipment efficiency in the oil and petrochemical industry. The gamma attenuation technique can be used as a non-invasive effective tool for detecting scale deposits in petroleum pipelines. The goal of this study is to propose a dual-energy gamma attenuation method with radial basis function neural network (RBFNN) to determine scale thickness in petroleum pipelines in which two-phase flows with different symmetrical flow regimes and void fractions exist. The detection system consists of a dual-energy gamma source, with Ba-133 and Cs-137 radioisotopes and two 2.54-cm × 2.54-cm sodium iodide (NaI) detectors to record photons. The first detector related to transmitted photons, and the second one to scattered photons. The transmission detector recorded two signals, which were the counts under photopeak of Ba-133 and Cs-137 with the energy of 356 keV and 662 keV, respectively. The one signal recorded in the scattering detector, total counts, was applied to RBFNN as the inputs, and scale thickness was assigned as the output.

Abstract. We evaluate the performance of different optimization techniques developed in the context of optical flow computation with different variational models. In particular, based on truncated Newton (TN) methods that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computing the optical flow. More precisely, we compare the performance of a standard unidirectional multilevel algorithm-called multiresolution optimization (MR/Opt)-with that of a bidirectional multilevel algorithm-called full multigrid optimization (FMG/Opt). The FMG/Opt algorithm treats the coarse grid correction as an optimization search direction and eventually scales it using a line search. Experimental results on three image sequences using four models of optical flow with different computational efforts show that the FMG/Opt algorithm outperforms both the TN and MR/Opt algorithms in terms of the computational work and the quality of the optical flow estimation.