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A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.
Qin S, Le X, Wang J. Qin S, et al. IEEE Trans Neural Netw Learn Syst. 2017 Nov;28(11):2580-2591. doi: 10.1109/TNNLS.2016.2595489. Epub 2016 Aug 19. IEEE Trans Neural Netw Learn Syst. 2017. PMID: 28113639
This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). ...
This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker …
Approximate weakly efficient solutions of set-valued vector equilibrium problems.
Chen J, Xu Y, Zhang K. Chen J, et al. J Inequal Appl. 2018;2018(1):181. doi: 10.1186/s13660-018-1773-0. Epub 2018 Jul 20. J Inequal Appl. 2018. PMID: 30137909 Free PMC article.
Under the assumption of near cone-subconvexlikeness, by using the separation theorem for convex sets we establish Kuhn-Tucker-type and Lagrange-type optimality conditions for set-valued vector equilibrium problems, respectively....
Under the assumption of near cone-subconvexlikeness, by using the separation theorem for convex sets we establish Kuhn-Tuck …
A minimum volume covering approach with a set of ellipsoids.
Martínez-Rego D, Castillo E, Fontenla-Romero O, Alonso-Betanzos A. Martínez-Rego D, et al. IEEE Trans Pattern Anal Mach Intell. 2013 Dec;35(12):2997-3009. doi: 10.1109/TPAMI.2013.94. IEEE Trans Pattern Anal Mach Intell. 2013. PMID: 24136436
Its main original features are: 1) It avoids the direct evaluation of determinants by using diagonalization properties of the involved matrices, 2) it identifies and removes outliers from the estimation process, 3) it avoids binary variables resulting from the combinatorial chara …
Its main original features are: 1) It avoids the direct evaluation of determinants by using diagonalization properties of the involved matri …
Optimal bidding strategy of a wind power producer in Chinese spot market considering green certificate trading.
Wu Q, Zhu X. Wu Q, et al. Environ Sci Pollut Res Int. 2024 Feb;31(9):13426-13441. doi: 10.1007/s11356-024-31965-3. Epub 2024 Jan 22. Environ Sci Pollut Res Int. 2024. PMID: 38246938
The upper level problem of the model describes the decision-making process of the wind power producer, and the lower level problems include the clearing process of the spot market and the TGC market, in which the spot market includes the day-ahead market and the balance market, a …
The upper level problem of the model describes the decision-making process of the wind power producer, and the lower level problems include …
K-means-type algorithms: a generalized convergence theorem and characterization of local optimality.
Selim SZ, Ismail MA. Selim SZ, et al. IEEE Trans Pattern Anal Mach Intell. 1984 Jan;6(1):81-7. doi: 10.1109/tpami.1984.4767478. IEEE Trans Pattern Anal Mach Intell. 1984. PMID: 21869168
It is shown that under certain conditions the algorithm may fail to converge to a local minimum, and that it converges under differentiability conditions to a Kuhn-Tucker point. Finally, a method for obtaining a local-minimum solution is given....
It is shown that under certain conditions the algorithm may fail to converge to a local minimum, and that it converges under differentiabili …
Smoothing inertial neurodynamic approach for sparse signal reconstruction via Lp-norm minimization.
Zhao Y, Liao X, He X, Tang R, Deng W. Zhao Y, et al. Neural Netw. 2021 Aug;140:100-112. doi: 10.1016/j.neunet.2021.02.006. Epub 2021 Feb 27. Neural Netw. 2021. PMID: 33752140
First, the problem is transformed into a smooth optimization problem based on smoothing approximation method, and the Lipschitz property of gradient of the smooth objective function is discussed. Then, SINA based on Karush-Kuhn-Tucker (KKT) condition, smoothing appr …
First, the problem is transformed into a smooth optimization problem based on smoothing approximation method, and the Lipschitz property of …
Mathematical formulation and analysis of the nonlinear system reconstruction of the online image-guided adaptive control of hyperthermia.
Cheng KS, Dewhirst MW, Stauffer PF, Das S. Cheng KS, et al. Med Phys. 2010 Mar;37(3):980-94. doi: 10.1118/1.3298005. Med Phys. 2010. PMID: 20384234 Free PMC article.
This clinical need motivates an analysis of the essential mathematical characteristics and constraints of such an approach. METHODS: The implicit function theorem (IFT), the Karush-Kuhn-Tucker (KKT) necessary condition of optimality, and the Tikhonov-Phillips …
This clinical need motivates an analysis of the essential mathematical characteristics and constraints of such an approach. METHODS: The imp …