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A novel machine-learning based optimization: identifying new treatment regimens for tuberculosis. 一种新的基于机器学习的优化：确定结核病的新治疗方案。
IF 1.1
Numerical Algebra Control and Optimization Pub Date : 2025-09-01 DOI: 10.3934/naco.2025025
Maral Budak, Pariksheet Nanda, Denise Kirschner
{"title":"A novel machine-learning based optimization: identifying new treatment regimens for tuberculosis.","authors":"Maral Budak, Pariksheet Nanda, Denise Kirschner","doi":"10.3934/naco.2025025","DOIUrl":"10.3934/naco.2025025","url":null,"abstract":"<p><p>Identifying optimization in a system from any discipline requires identifying ways to either maximize or minimize objectives of interest-or even trade-offs between these choices where goals must be balanced. Traditionally, optimal control theory has been used specifically for applications that are represented by ordinary differential equations. Here, we introduce a new approach to optimization that can be applied not only to ordinary differential-equation based systems, but importantly to other more complex models, such as agent-based model systems. To this end, we create a novel machine learning optimization pipeline that uses a Kriging-based surrogate model to predict objective functions. We use a Pareto optimization algorithm to identify regimens that maximize improvement to the predicted optimal set and then rank these findings. As an example, we apply this to a model system that captures drug treatment of hosts during infection with <i>Mycobacterium tuberculosis.</i> Typically for treatment of tuberculosis, a multiple drug regimen is used where four antibiotics are administered for a lengthy time frame of 6-9 months. We apply our new method to optimize treatment in the face of many choices for drugs, combinations and dosages and link for the first time with rankings to the optimized set of outcomes.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12637175/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145589124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi Strongly $ E $-preinvexity and its relationships with non-linear programming 拟强$ E $-先验性及其与非线性规划的关系
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2023-01-18 DOI: 10.3934/naco.2023010
Akhlad Iqbal, Askar Hussain
{"title":"Quasi Strongly $ E $-preinvexity and its relationships with non-linear programming","authors":"Akhlad Iqbal, Askar Hussain","doi":"10.3934/naco.2023010","DOIUrl":"https://doi.org/10.3934/naco.2023010","url":null,"abstract":"In this paper, we extend the class of strongly $E$-preinvex and strongly $E$-invex functions to quasi strongly $E$-preinvex, quasi strongly $E$-invex and pseudo strongly $E$-invex functions. Some nontrivial suitable examples have been constructed in support of our definitions. Several interesting properties and relationships of these functions are discussed. Furthermore, to show the application of our results, we consider a nonlinear programming problem and show that the local minimum point is also a strictly global minimum.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77226755","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
Mean-field type quadratic BSDEs 平均场型二次BSDEs
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2022009
Hélène Hibon, Ying Hu, Shanjian Tang
{"title":"Mean-field type quadratic BSDEs","authors":"Hélène Hibon, Ying Hu, Shanjian Tang","doi":"10.3934/naco.2022009","DOIUrl":"https://doi.org/10.3934/naco.2022009","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean. The general case can be treated by a fixed point argument.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136092720","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: 3
Optimization method in counter terrorism: min-max zero-sum differential game approach 反恐最优化方法:最小-最大零和微分对策方法
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2022013
Abd El-Monem A. Megahed, Ebrahim A. Youness, Hebatallah K. Arafat
{"title":"Optimization method in counter terrorism: min-max zero-sum differential game approach","authors":"Abd El-Monem A. Megahed, Ebrahim A. Youness, Hebatallah K. Arafat","doi":"10.3934/naco.2022013","DOIUrl":"https://doi.org/10.3934/naco.2022013","url":null,"abstract":"One of the most critical problems facing governments at present is terrorism. Most recent studies are striving to find an optimal solution to this problem that threatens the security and stability of people. To combat terrorism, government uses various means, such as improving education quality, providing labor opportunities, seeking social justice, creating religious awareness, and building security arrangements. This study aims to evaluate the optimum strategy for both government and terrorist organization using a min-max zero-sum differential game approach. In addition, it analyses the dynamics of the government's activities separately and explain the impact of the government's counter-terror measures on the activity and strength of international terror organization.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"323 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136296833","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
Going forward & backward with Jin Ma 和金马一起前进和后退
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2023005
P. Protter
{"title":"Going forward & backward with Jin Ma","authors":"P. Protter","doi":"10.3934/naco.2023005","DOIUrl":"https://doi.org/10.3934/naco.2023005","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"7 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78381824","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 inertial three-term hybrid CG-based projection method for constrained nonlinear pseudo-monotone equations with applications 约束非线性伪单调方程的一种惯性三项混合cg投影方法及其应用
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2023009
Yue Zhuo, Xiaoyu Wu, Jincheng Zhou
{"title":"An inertial three-term hybrid CG-based projection method for constrained nonlinear pseudo-monotone equations with applications","authors":"Yue Zhuo, Xiaoyu Wu, Jincheng Zhou","doi":"10.3934/naco.2023009","DOIUrl":"https://doi.org/10.3934/naco.2023009","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"24 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75569364","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
Variations of orthonormal basis matrices of subspaces 子空间的正交基矩阵的变分
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2023021
Zhongming Teng, Ren-Cang Li
{"title":"Variations of orthonormal basis matrices of subspaces","authors":"Zhongming Teng, Ren-Cang Li","doi":"10.3934/naco.2023021","DOIUrl":"https://doi.org/10.3934/naco.2023021","url":null,"abstract":"An orthonormal basis matrix $ X $ of a subspace $ {mathcal X} $ is known not to be unique, unless there are some kinds of normalization requirements. One of them is to require that $ X^{ text{T}}D $ is positive semi-definite, where $ D $ is a constant matrix of apt size. It is a natural one in multi-view subspace learning models in which $ X $ serves as a projection matrix and is determined by a maximization problem over the Stiefel manifold whose objective function contains and increases with $ text{tr}(X^{ text{T}}D) $. This paper is concerned with bounding the change in orthonormal basis matrix $ X $ as subspace $ {mathcal X} $ varies under the requirement that $ X^{ text{T}}D $ stays positive semi-definite. The results are useful in convergence analysis of the NEPv approach (nonlinear eigenvalue problem with eigenvector dependency) to solve the maximization problem.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135440832","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
Convergence analysis of multiple-sets split equality common fixed point problem with applications 多集分裂等式公共不动点问题的收敛性分析及其应用
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2023012
N. Gupta, L. Jolaoso, Ashish Nandal, R. Chugh
{"title":"Convergence analysis of multiple-sets split equality common fixed point problem with applications","authors":"N. Gupta, L. Jolaoso, Ashish Nandal, R. Chugh","doi":"10.3934/naco.2023012","DOIUrl":"https://doi.org/10.3934/naco.2023012","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"32 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82710392","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
A brief discussion about a predator-prey model including disease in predators with the delay effect 一个包含延迟效应的捕食者疾病的捕食者-猎物模型的简要讨论
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2023018
Debashis Das, Sarbani Chakraborty
{"title":"A brief discussion about a predator-prey model including disease in predators with the delay effect","authors":"Debashis Das, Sarbani Chakraborty","doi":"10.3934/naco.2023018","DOIUrl":"https://doi.org/10.3934/naco.2023018","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"33 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85566248","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
Superhedging problem under ratio constraint: BSDE approaches with Malliavin calculus 比率约束下的超套期保值问题:带有Malliavin微积分的BSDE方法
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2023-01-01 DOI: 10.3934/naco.2023007
Mingyu Xu
{"title":"Superhedging problem under ratio constraint: BSDE approaches with Malliavin calculus","authors":"Mingyu Xu","doi":"10.3934/naco.2023007","DOIUrl":"https://doi.org/10.3934/naco.2023007","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"16 1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78328151","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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