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Dehomogenization for completely positive tensors 完全正张量的非均质化
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-06-25 DOI: 10.3934/naco.2022037
Jiawang Nie, Xindong Tang, Zi Yang, Suhan Zhong
{"title":"Dehomogenization for completely positive tensors","authors":"Jiawang Nie, Xindong Tang, Zi Yang, Suhan Zhong","doi":"10.3934/naco.2022037","DOIUrl":"https://doi.org/10.3934/naco.2022037","url":null,"abstract":". A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the deho- mogenization approach.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79664111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Approximation of $ N $-player stochastic games with singular controls by mean field games 用平均场对策逼近具有奇异控制的N人随机对策
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-02-14 DOI: 10.3934/naco.2023001
Haoyang Cao, Xin Guo, Joon Seok Lee
{"title":"Approximation of $ N $-player stochastic games with singular controls by mean field games","authors":"Haoyang Cao, Xin Guo, Joon Seok Lee","doi":"10.3934/naco.2023001","DOIUrl":"https://doi.org/10.3934/naco.2023001","url":null,"abstract":"This paper establishes that a class of $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More specifically, it shows (i) the optimal control to an MFG with singular controls of a bounded velocity $theta$ is shown to be an $epsilon_N$-NE to an $N$-player game with singular controls of the bounded velocity, with $epsilon_N = O(frac{1}{sqrt{N}})$, and (ii) the optimal control to this MFG is an $(epsilon_N + epsilon_{theta})$-NE to an $N$-player game with singular controls of finite variation, where $epsilon_{theta}$ is an error term that depends on $theta$. This work generalizes the classical result on approximation $N$-player games by MFGs, by allowing for discontinuous controls.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"10 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77342384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Random sets and Choquet-type representations 随机集和choquet型表示
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-16 DOI: 10.3934/naco.2023008
cCaugin Ararat, Umur Cetin
{"title":"Random sets and Choquet-type representations","authors":"cCaugin Ararat, Umur Cetin","doi":"10.3934/naco.2023008","DOIUrl":"https://doi.org/10.3934/naco.2023008","url":null,"abstract":"As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, Choquet decompositions and Choquet convex decompositions, as well as their corresponding hull operators acting on the power sets of Lebesgue-Bochner spaces. We show that Choquet hull coincides with convex hull in the finite-dimensional setting, yet Choquet hull tends to be larger in infinite dimensions. We also provide a quantitative characterization of Choquet hull. Furthermore, we show that Choquet decomposable hull of a set coincides with its (strongly) closed decomposable hull and the Choquet convex decomposable hull of a set coincides with its Choquet decomposable hull of the convex hull. It turns out that the collection of all measurable selections of a closed-valued multifunction is Choquet decomposable and those of a closed convex-valued multifunction is Choquet convex decomposable. Finally, we investigate the operator-type features of Choquet decomposable and Choquet convex decomposable hull operators when applied in succession.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"31 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91384043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Forward-backward stochastic differential equations: Initiation, development and beyond 正反向随机微分方程:开始、发展及以后
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2022011
J. Yong
{"title":"Forward-backward stochastic differential equations: Initiation, development and beyond","authors":"J. Yong","doi":"10.3934/naco.2022011","DOIUrl":"https://doi.org/10.3934/naco.2022011","url":null,"abstract":"<p style='text-indent:20px;'>Jin Ma has made fundamental contributions to the theory of forward-backward stochastic differential equations (FBSDEs, for short). In this paper, as one of his main collaborators, I will recall the initiation, the path of the development for FBSDEs, as well as some interesting historic stories.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"40 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88483597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An improved projection algorithm for variational inequality problem with multivalued mapping 多值映射变分不等式问题的一种改进投影算法
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2022002
Ouafa Belguidoum, Hassina Grar
{"title":"An improved projection algorithm for variational inequality problem with multivalued mapping","authors":"Ouafa Belguidoum, Hassina Grar","doi":"10.3934/naco.2022002","DOIUrl":"https://doi.org/10.3934/naco.2022002","url":null,"abstract":"In this paper, we propose a new projection method (extragradient method) for solving the generalized variational inequality problem. Our method is well-defined and is proven to be globally convergent to a solution of the problem under the assumptions that the multivalued mapping is continuous and satisfies a condition that is strictly weaker than the pseudomonotonicity. Finally, to support our results and to illustrate the numerical behavior of the proposed algorithm, some fundamental experiments are provided and also compared with recent works.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"70 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76242225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Modeling the relationship between outdoor meteorological data and energy consumptions at heating and cooling periods: Application in a university building 室外气象数据与冷暖期能耗关系的建模:在某高校建筑中的应用
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2022021
O. Kon, B. Yuksel, A. D. Karaoglan
{"title":"Modeling the relationship between outdoor meteorological data and energy consumptions at heating and cooling periods: Application in a university building","authors":"O. Kon, B. Yuksel, A. D. Karaoglan","doi":"10.3934/naco.2022021","DOIUrl":"https://doi.org/10.3934/naco.2022021","url":null,"abstract":"In this study regression modeling is proposed for calculating the heating and cooling load of the buildings by considering the outdoor meteorological data. For this pupose, Balikesir University Rectorate Building is selected as the case building. In the winter months, measurements were made in the hot water boiler in the basement of the building for the heating energy load. For the cooling energy load, measurements were made in the chiller groups near the building. As climate data, eight variables were considered: outdoor temperature, solar radiation, relative humidity, wind speed, atmospheric pressure, sunshine duration, steam pressure, and 1 m underground temperature. The Minitab statistical analysis program was used to perform the modeling. 55 samples were used for mathematically modeling the heating load, while 37 samples are used for modeling the cooling load. The Rbegin{document}$ {}^{2 } $end{document}(coefficient of determination) values are calculated as 96.2% and 98.94% for cooling load and heating load, respectively. In addition to these findings, ANOVA results for both models were examined and both models were found to be significant.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81476654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An active set solver for constrained $ H_infty $ optimal control problems with state and input constraints 具有状态约束和输入约束的受限$ H_infty $最优控制问题的主动集求解器
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2021056
Canghua Jiang, Dongming Zhang, Chi Yuan, K. L. Teo
{"title":"An active set solver for constrained $ H_infty $ optimal control problems with state and input constraints","authors":"Canghua Jiang, Dongming Zhang, Chi Yuan, K. L. Teo","doi":"10.3934/naco.2021056","DOIUrl":"https://doi.org/10.3934/naco.2021056","url":null,"abstract":"This paper proposes an active set solver for begin{document}$ H_infty $end{document} min-max optimal control problems involving linear discrete-time systems with linearly constrained states, controls and additive disturbances. The proposed solver combines Riccati recursion with dynamic programming. To deal with possible degeneracy (i.e. violations of the linear independence constraint qualification), constraint transformations are introduced that allow the surplus equality constraints on the state at each stage to be moved to the previous stage together with their Lagrange multipliers. In this way, degeneracy for a feasible active set can be determined by checking whether there exists an equality constraint on the initial state over the prediction horizon. For situations when the active set is degenerate and all active constraints indexed by it are non-redundant, a vertex exploration strategy is developed to seek a non-degenerate active set. If the sampled state resides in a robust control invariant set and certain second-order sufficient conditions are satisfied at each stage, then a bounded begin{document}$ l_2 $end{document} gain from the disturbance to controlled output can be guaranteed for the closed-loop system under some standard assumptions. Theoretical analysis and numerical simulations show that the computational complexity per iteration of the proposed solver depends linearly on the prediction horizon.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"22 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82635824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distributionally Robust Optimization: A review on theory and applications 分布鲁棒优化:理论与应用综述
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2021057
Fengming Lin, X. Fang, Zheming Gao
{"title":"Distributionally Robust Optimization: A review on theory and applications","authors":"Fengming Lin, X. Fang, Zheming Gao","doi":"10.3934/naco.2021057","DOIUrl":"https://doi.org/10.3934/naco.2021057","url":null,"abstract":"In this paper, we survey the primary research on the theory and applications of distributionally robust optimization (DRO). We start with reviewing the modeling power and computational attractiveness of DRO approaches, induced by the ambiguity sets structure and tractable robust counterpart reformulations. Next, we summarize the efficient solution methods, out-of-sample performance guarantee, and convergence analysis. Then, we illustrate some applications of DRO in machine learning and operations research, and finally, we discuss the future research directions.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82948344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 52
Exact controllability for a degenerate and singular wave equation with moving boundary 一类带运动边界的简并奇异波动方程的精确可控性
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2022001
Alhabib Moumni, J. Salhi
{"title":"Exact controllability for a degenerate and singular wave equation with moving boundary","authors":"Alhabib Moumni, J. Salhi","doi":"10.3934/naco.2022001","DOIUrl":"https://doi.org/10.3934/naco.2022001","url":null,"abstract":"This paper is concerned with the exact boundary controllability for a degenerate and singular wave equation in a bounded interval with a moving endpoint. By the multiplier method and using an adapted Hardy-poincaré inequality, we prove direct and inverse inequalities for the solutions of the associated adjoint equation. As a consequence, by the Hilbert Uniqueness Method, we deduce the controllability result of the considered system when the control acts on the moving boundary. Furthermore, improved estimates of the speed of the moving endpoint and the controllability time are obtained.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82617832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Double stranded smoothing technique in energy minimization problems 能量最小化问题中的双链平滑技术
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI: 10.3934/naco.2022022
A. Sahiner, Nurullah Yilmaz
{"title":"Double stranded smoothing technique in energy minimization problems","authors":"A. Sahiner, Nurullah Yilmaz","doi":"10.3934/naco.2022022","DOIUrl":"https://doi.org/10.3934/naco.2022022","url":null,"abstract":"In this study, we propose a new algorithm for image denoising by using double stranded Bezier curves based smoothing technique. The algorithm is developed to solve energy minimization problems with non-smooth total variation norm (TV). In order to demonstrate the efficiency of the algorithm we apply it to some numerical examples. The experimental results are reported and they are compared with the results obtained from TV algorithm with hyperbolic smoothing and standard TV algorithm.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"60 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83769081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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