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A path following algorithm for infinite quadratic programming on a Hilbert space
1.  Department of Electrical & Electronic Engineering, University of Melbourne, Parkville Victoria 3052, Australia 
2.  Department of Systems Engineering, Australian National University, Canberra A.C.T. 0200, Australia 
[1] 
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399413. doi: 10.3934/jimo.2007.3.399 
[2] 
Liming Sun, LiZhi Liao. An interior point continuous pathfollowing trajectory for linear programming. Journal of Industrial & Management Optimization, 2018, 13 (5) : 118. doi: 10.3934/jimo.2018107 
[3] 
Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming formulations of deterministic infinite horizon optimal control problems in discrete time. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 38213838. doi: 10.3934/dcdsb.2017192 
[4] 
Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time. Discrete & Continuous Dynamical Systems  B, 2019, 24 (4) : 17431767. doi: 10.3934/dcdsb.2018235 
[5] 
Ardeshir Ahmadi, Hamed DavariArdakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359377. doi: 10.3934/naco.2017023 
[6] 
Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 115. doi: 10.3934/jimo.2008.4.1 
[7] 
Paul B. Hermanns, Nguyen Van Thoai. Global optimization algorithm for solving bilevel programming problems with quadratic lower levels. Journal of Industrial & Management Optimization, 2010, 6 (1) : 177196. doi: 10.3934/jimo.2010.6.177 
[8] 
Yanqin Bai, Pengfei Ma, Jing Zhang. A polynomialtime interiorpoint method for circular cone programming based on kernel functions. Journal of Industrial & Management Optimization, 2016, 12 (2) : 739756. doi: 10.3934/jimo.2016.12.739 
[9] 
Soodabeh Asadi, Hossein Mansouri. A Mehrotra type predictorcorrector interiorpoint algorithm for linear programming. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 147156. doi: 10.3934/naco.2019011 
[10] 
Boshi Tian, Xiaoqi Yang, Kaiwen Meng. An interiorpoint $l_{\frac{1}{2}}$penalty method for inequality constrained nonlinear optimization. Journal of Industrial & Management Optimization, 2016, 12 (3) : 949973. doi: 10.3934/jimo.2016.12.949 
[11] 
Ziye Shi, Qingwei Jin. Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 871882. doi: 10.3934/jimo.2014.10.871 
[12] 
Yanqin Bai, Xuerui Gao, Guoqiang Wang. Primaldual interiorpoint algorithms for convex quadratic circular cone optimization. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 211231. doi: 10.3934/naco.2015.5.211 
[13] 
Yanqin Bai, Lipu Zhang. A fullNewton step interiorpoint algorithm for symmetric cone convex quadratic optimization. Journal of Industrial & Management Optimization, 2011, 7 (4) : 891906. doi: 10.3934/jimo.2011.7.891 
[14] 
Yongjian Yang, Zhiyou Wu, Fusheng Bai. A filled function method for constrained nonlinear integer programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 353362. doi: 10.3934/jimo.2008.4.353 
[15] 
Silvia Faggian. Boundary control problems with convex cost and dynamic programming in infinite dimension part II: Existence for HJB. Discrete & Continuous Dynamical Systems  A, 2005, 12 (2) : 323346. doi: 10.3934/dcds.2005.12.323 
[16] 
Guoqiang Wang, Zhongchen Wu, Zhongtuan Zheng, Xinzhong Cai. Complexity analysis of primaldual interiorpoint methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 101113. doi: 10.3934/naco.2015.5.101 
[17] 
Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 24732485. doi: 10.3934/cpaa.2012.11.2473 
[18] 
Yanqun Liu, MingFang Ding. A ladder method for linear semiinfinite programming. Journal of Industrial & Management Optimization, 2014, 10 (2) : 397412. doi: 10.3934/jimo.2014.10.397 
[19] 
Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 10271039. doi: 10.3934/jimo.2011.7.1027 
[20] 
Bao Qing Hu, Song Wang. A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions. Journal of Industrial & Management Optimization, 2006, 2 (4) : 373385. doi: 10.3934/jimo.2006.2.373 
2017 Impact Factor: 1.179
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