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1.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
2.
3.
Sze-Jack Tan Chee-Keong Lee Chee-Yuen Gan Olusegun Abayomi Olalere 《Molecules (Basel, Switzerland)》2021,26(7)
In this study, the combination of parameters required for optimal extraction of anti-oxidative components from the Chinese lotus (CLR) and Malaysian lotus (MLR) roots were carefully investigated. Box–Behnken design was employed to optimize the pH (X1: 2–3), extraction time (X2: 0.5–1.5 h) and solvent-to-sample ratio (X3: 20–40 mL/g) to obtain a high flavonoid yield with high % DPPHsc free radical scavenging and Ferric-reducing power assay (FRAP). The analysis of variance clearly showed the significant contribution of quadratic model for all responses. The optimal conditions for both Chinese lotus (CLR) and Malaysian lotus (MLR) roots were obtained as: CLR: X1 = 2.5; X2 = 0.5 h; X3 = 40 mL/g; MLR: X1 = 2.4; X2 = 0.5 h; X3 = 40 mL/g. These optimum conditions gave (a) Total flavonoid content (TFC) of 0.599 mg PCE/g sample and 0.549 mg PCE/g sample, respectively; (b) % DPPHsc of 48.36% and 29.11%, respectively; (c) FRAP value of 2.07 mM FeSO4 and 1.89 mM FeSO4, respectively. A close agreement between predicted and experimental values was found. The result obtained succinctly revealed that the Chinese lotus exhibited higher antioxidant and total flavonoid content when compared with the Malaysia lotus root at optimum extraction condition. 相似文献
4.
5.
Ji-Ming Peng 《Mathematical Programming》1997,78(3):347-355
In this paper we propose a class of merit functions for variational inequality problems (VI). Through these merit functions,
the variational inequality problem is cast as unconstrained minimization problem. We estimate the growth rate of these merit
functions and give conditions under which the stationary points of these functions are the solutions of VI.
This work was supported by the state key project “Scientific and Engineering Computing”. 相似文献
6.
HIRONOBU Ishihara 《Geometriae Dedicata》1997,67(3):309-336
Several classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank 2 ample vector bundles with c2 less than seven on Hirzebruch surfaces, and with c2 less than four on Del Pezzo surfaces. 相似文献
7.
An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines 总被引:2,自引:0,他引:2
Luca Zanni 《Computational Management Science》2006,3(2):131-145
In this paper we propose some improvements to a recent decomposition technique for the large quadratic program arising in
training support vector machines. As standard decomposition approaches, the technique we consider is based on the idea to
optimize, at each iteration, a subset of the variables through the solution of a quadratic programming subproblem. The innovative
features of this approach consist in using a very effective gradient projection method for the inner subproblems and a special
rule for selecting the variables to be optimized at each step. These features allow to obtain promising performance by decomposing
the problem into few large subproblems instead of many small subproblems as usually done by other decomposition schemes. We
improve this technique by introducing a new inner solver and a simple strategy for reducing the computational cost of each
iteration. We evaluate the effectiveness of these improvements by solving large-scale benchmark problems and by comparison
with a widely used decomposition package. 相似文献
8.
9.
Well-Posedness by Perturbations of Variational Problems 总被引:3,自引:0,他引:3
Lemaire B. Ould Ahmed Salem C. Revalski J. P. 《Journal of Optimization Theory and Applications》2002,115(2):345-368
In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented. 相似文献
10.
Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak
estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum,
minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity
networks is considered.
Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002 相似文献