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Optimization: algorithms and consistent approximationsJune 1997
- Author:
- Elijah Polak
Abstract
No abstract available.
Cited By
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- Zhang C, Liu Z, Hong T and Zhang G (2019). Interference alignment schemes for k-user interference channel based on manifold optimization, EURASIP Journal on Wireless Communications and Networking, 2019:1, (1-11), Online publication date: 1-Dec-2019.
- Dolgopolik M (2018). A convergence analysis of the method of codifferential descent, Computational Optimization and Applications, 71:3, (879-913), Online publication date: 1-Dec-2018.
- Royset J (2018). Approximations and solution estimates in optimization, Mathematical Programming: Series A and B, 170:2, (479-506), Online publication date: 1-Aug-2018.
- Noori Skandari M and Ghaznavi M (2018). A numerical method for solving shortest path problems, Calcolo: a quarterly on numerical analysis and theory of computation, 55:1, (1-18), Online publication date: 1-Mar-2018.
Ali U and Egerstedt M (2018). Hybrid Optimal Control under Mode Switching Constraints with Applications to Pesticide Scheduling, ACM Transactions on Cyber-Physical Systems, 2:1, (1-17), Online publication date: 31-Jan-2018.- Cherrak O, Ghennioui H, Thirion-Moreau N and Abarkan E (2018). Preconditioned optimization algorithms solving the problem of the non unitary joint block diagonalization, Multidimensional Systems and Signal Processing, 29:4, (1373-1396), Online publication date: 1-Oct-2018.
- Chen H and Zhang W (2017). On weak topology for optimal control of switched nonlinear systems, Automatica (Journal of IFAC), 81:C, (409-415), Online publication date: 1-Jul-2017.
- Royset J and Wets R (2016). Optimality Functions and Lopsided Convergence, Journal of Optimization Theory and Applications, 169:3, (965-983), Online publication date: 1-Jun-2016.
- Mayne D and Falugi P (2016). Generalized Stabilizing Conditions for Model Predictive Control, Journal of Optimization Theory and Applications, 169:3, (719-734), Online publication date: 1-Jun-2016.
- Seidl R and Rank E (2016). Iterative time reversal based flaw identification, Computers & Mathematics with Applications, 72:4, (879-892), Online publication date: 1-Aug-2016.
- Khong S, Nešić D and Krstić M (2016). Iterative learning control based on extremum seeking, Automatica (Journal of IFAC), 66:C, (238-245), Online publication date: 1-Apr-2016.
- Zhang Y and Hirakawa K (2016). Blind Deblurring and Denoising of Images Corrupted by Unidirectional Object Motion Blur and Sensor Noise, IEEE Transactions on Image Processing, 25:9, (4129-4144), Online publication date: 1-Sep-2016.
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- Bajc I, Hecht F and źumer S (2016). A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency, Journal of Computational Physics, 321:C, (981-996), Online publication date: 15-Sep-2016.
- Meng Z, Pan J and Alelaiwi A (2016). A new meta-heuristic ebb-tide-fish-inspired algorithm for traffic navigation, Telecommunications Systems, 62:2, (403-415), Online publication date: 1-Jun-2016.
- Polak E, Lee S, Bustany I and Madhan A (2016). Method of Outer Approximations and Adaptive Approximations for a Class of Matrix Games, Journal of Optimization Theory and Applications, 170:3, (876-899), Online publication date: 1-Sep-2016.
- Royset J (2016). Preface, Journal of Optimization Theory and Applications, 169:3, (713-718), Online publication date: 1-Jun-2016.
- Yang X, Chen Z and Zhou J (2016). Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions, Journal of Optimization Theory and Applications, 169:3, (984-1012), Online publication date: 1-Jun-2016.
- Gong Q, Ross I and Fahroo F (2016). Spectral and Pseudospectral Optimal Control Over Arbitrary Grids, Journal of Optimization Theory and Applications, 169:3, (759-783), Online publication date: 1-Jun-2016.
- Kirst P and Stein O (2016). Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques, Journal of Optimization Theory and Applications, 169:3, (1079-1109), Online publication date: 1-Jun-2016.
- El-Gebeily M, Mordukhovich B and Alshahrani M (2016). Optimal Control of Constrained Self-Adjoint Nonlinear Operator Equations in Hilbert Spaces, Journal of Optimization Theory and Applications, 169:3, (735-758), Online publication date: 1-Jun-2016.
- Laurière M and Pironneau O (2016). Dynamic Programming for Mean-Field Type Control, Journal of Optimization Theory and Applications, 169:3, (902-924), Online publication date: 1-Jun-2016.
- Foraker J, Royset J and Kaminer I (2016). Search-Trajectory Optimization, Journal of Optimization Theory and Applications, 169:2, (550-567), Online publication date: 1-May-2016.
- Jones A, Ali U and Egerstedt M Optimal pesticide scheduling in precision agriculture Proceedings of the 7th International Conference on Cyber-Physical Systems, (1-8)
- De Mulder W, Bethard S and Moens M (2015). A survey on the application of recurrent neural networks to statistical language modeling, Computer Speech and Language, 30:1, (61-98), Online publication date: 1-Mar-2015.
- Khong S, Tan Y, Manzie C and Nešić D (2015). Extremum seeking of dynamical systems via gradient descent and stochastic approximation methods, Automatica (Journal of IFAC), 56:C, (44-52), Online publication date: 1-Jun-2015.
- Kmet T and Kmetova M (2015). Adaptive critic design and Hopfield neural network based simulation of time delayed photosynthetic production and prey-predator model, Information Sciences: an International Journal, 294:C, (586-599), Online publication date: 10-Feb-2015.
- Phelps C, Gong Q, Royset J, Walton C and Kaminer I (2014). Consistent approximation of a nonlinear optimal control problem with uncertain parameters, Automatica (Journal of IFAC), 50:12, (2987-2997), Online publication date: 1-Dec-2014.
- Duarte B and Tsoukalas A (2014). Solving quality control problems with an algorithm for minimax programs with coupled constraints, Computers and Operations Research, 41, (223-230), Online publication date: 1-Jan-2014.
- Chandrasekaran V, Recht B, Parrilo P and Willsky A (2012). The Convex Geometry of Linear Inverse Problems, Foundations of Computational Mathematics, 12:6, (805-849), Online publication date: 1-Dec-2012.
- Adanhounmè V, Dagba T and Adédjouma S Neural smooth function approximation and prediction with adaptive learning rate Transactions on Computational Collective Intelligence VII, (103-118)
- Royset J and Pee E (2012). Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems, Journal of Optimization Theory and Applications, 155:3, (855-882), Online publication date: 1-Dec-2012.
- Spall J (2012). Cyclic Seesaw Process for Optimization and Identification, Journal of Optimization Theory and Applications, 154:1, (187-208), Online publication date: 1-Jul-2012.
- Stein O and Steuermann P (2012). The adaptive convexification algorithm for semi-infinite programming with arbitrary index sets, Mathematical Programming: Series A and B, 136:1, (183-207), Online publication date: 1-Dec-2012.
- Royset J (2012). Optimality functions in stochastic programming, Mathematical Programming: Series A and B, 135:1-2, (293-321), Online publication date: 1-Oct-2012.
- Kmet T and Kmetova M Neural networks solving free final time optimal control problem Proceedings of the First international conference on Theory and Practice of Natural Computing, (174-186)
- Kmet T Neural network solution of optimal control problem with control and state constraints Proceedings of the 21st international conference on Artificial neural networks - Volume Part II, (261-268)
- Gonzalez H, Vasudevan R, Kamgarpour M, Sastry S, Bajcsy R and Tomlin C A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems Proceedings of the 13th ACM international conference on Hybrid systems: computation and control, (51-60)
- Pham D, Bui H and Venkatesh S (2010). Bayesian minimax estimation of the normal model with incomplete prior covariance matrix specification, IEEE Transactions on Information Theory, 56:12, (6433-6449), Online publication date: 1-Dec-2010.
- Gonzalez H and Polak E (2010). On the Perpetual Collision-Free RHC of Fleets of Vehicles, Journal of Optimization Theory and Applications, 145:1, (76-92), Online publication date: 1-Apr-2010.
- Chung H, Polak E and Sastry S (2010). On the Use of Outer Approximations as an External Active Set Strategy, Journal of Optimization Theory and Applications, 146:1, (51-75), Online publication date: 1-Jul-2010.
- Dagba T, Adanhounmè V and Adédjouma S Neural networks for solving the superposition problem using approximation method and adaptive learning rate Proceedings of the 4th KES international conference on Agent and multi-agent systems: technologies and applications, Part II, (92-99)
- Zhang F and Hancock E (2010). New Riemannian techniques for directional and tensorial image data, Pattern Recognition, 43:4, (1590-1606), Online publication date: 1-Apr-2010.
- Qi L, Ling C, Tong X and Zhou G (2009). A smoothing projected Newton-type algorithm for semi-infinite programming, Computational Optimization and Applications, 42:1, (1-30), Online publication date: 1-Jan-2009.
- Balasubramaniam P and Vincent Antony Kumar A (2009). Solution of matrix Riccati differential equation for nonlinear singular system using genetic programming, Genetic Programming and Evolvable Machines, 10:1, (71-89), Online publication date: 1-Mar-2009.
- Tricaud C and Chen Y Optimal mobile actuator/sensor network motion strategy for parameter estimation in a class of cyber physical systems Proceedings of the 2009 conference on American Control Conference, (367-372)
- Pennanen T (2009). Epi-convergent discretizations of multistage stochastic programs via integration quadratures, Mathematical Programming: Series A and B, 116:1-2, (461-479), Online publication date: 1-Jan-2009.
- Polak E, Womersley R and Yin H (2008). An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems, Journal of Optimization Theory and Applications, 138:2, (311-328), Online publication date: 1-Aug-2008.
- Polak E (2008). On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy, Journal of Optimization Theory and Applications, 138:2, (305-309), Online publication date: 1-Aug-2008.
- Ye J and Wu S (2008). First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems, Journal of Optimization Theory and Applications, 137:2, (419-434), Online publication date: 1-May-2008.
- Lan H (2008). An approach for solving fuzzy implicit variational inequalities with linear membership functions, Computers & Mathematics with Applications, 55:3, (563-572), Online publication date: 1-Feb-2008.
- Alaiz-Rodríguez R, Guerrero-Curieses A and Cid-Sueiro J (2007). Minimax Regret Classifier for Imprecise Class Distributions, The Journal of Machine Learning Research, 8, (103-130), Online publication date: 1-May-2007.
- Wardi Y, Ding X and Azuma S On-line optimization of switched-mode hybrid dynamical systems Proceedings of the 10th international conference on Hybrid systems: computation and control, (771-774)
- González-Dávila E, Dorta-Guerra R and Ginebra J (2007). Simulation-based designs for multiperiod control, Computational Statistics & Data Analysis, 51:12, (6624-6641), Online publication date: 1-Aug-2007.
- Martorella M, Berizzi F and Bruscoli S (2006). Use of genetic algorithms for contrast and entropy optimization in ISAR autofocusing, EURASIP Journal on Advances in Signal Processing, 2006, (133-133), Online publication date: 1-Jan-2006.
- Ji H and Fermuller C (2006). A 3D Shape Constraint on Video, IEEE Transactions on Pattern Analysis and Machine Intelligence, 28:6, (1018-1023), Online publication date: 1-Jun-2006.
- Xiong M, Liang B, Lam K and Guo Y (2006). Quality of Service Guarantee for Temporal Consistency of Real-Time Transactions, IEEE Transactions on Knowledge and Data Engineering, 18:8, (1097-1110), Online publication date: 1-Aug-2006.
- Chryssoverghi I, Coletsos I and Kokkinis B (2006). Discretization methods for optimal control problems with state constraints, Journal of Computational and Applied Mathematics, 191:1, (1-31), Online publication date: 15-Jun-2006.
- Mayne D, Raković S, Vinter R and Kerrigan E (2006). Characterization of the solution to a constrained H∞ optimal control problem, Automatica (Journal of IFAC), 42:3, (371-382), Online publication date: 1-Mar-2006.
- Boccadoro M, Wardi Y, Egerstedt M and Verriest E (2005). Optimal Control of Switching Surfaces in Hybrid Dynamical Systems, Discrete Event Dynamic Systems, 15:4, (433-448), Online publication date: 1-Dec-2005.
- Chryssoverghi I Discretization-optimization methods for optimal control problems Proceedings of the 5th WSEAS international conference on Simulation, modelling and optimization, (419-426)
- Noll D and Apkarian P (2005). Spectral bundle methods for non-convex maximum eigenvalue functions, Mathematical Programming: Series A and B, 104:2-3, (701-727), Online publication date: 1-Nov-2005.
- Noll D and Apkarian P (2005). Spectral bundle methods for non-convex maximum eigenvalue functions, Mathematical Programming: Series A and B, 104:2-3, (729-747), Online publication date: 1-Nov-2005.
- Chryssoverghi I Approximate gradient/penalty methods with general discretization schemes for optimal control problems Proceedings of the 5th international conference on Large-Scale Scientific Computing, (199-207)
- Shi Z and Shen J (2004). A gradient-related algorithm with inexact line searches, Journal of Computational and Applied Mathematics, 170:2, (349-370), Online publication date: 15-Sep-2004.
- Chryssoverghi I, Coletsos J and Kokkinis B (2004). Approximate Gradient Projection Method with Runge-Kutta Schemes for Optimal Control Problems, Computational Optimization and Applications, 29:1, (91-115), Online publication date: 1-Oct-2004.
- Royset J and Polak E (2004). Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations, Journal of Optimization Theory and Applications, 122:1, (157-184), Online publication date: 1-Jul-2004.
- Sheu R and Lin J (2004). Solving Continuous Min-Max Problems by an Iterative Entropic Regularization Method, Journal of Optimization Theory and Applications, 121:3, (597-612), Online publication date: 1-Jun-2004.
- Chryssoverghi I Progressively refining discrete gradient projection method for semilinear parabolic optimal control problems Proceedings of the Third international conference on Numerical Analysis and its Applications, (240-248)
- Malengier B Parameter estimation of si diffusion in fe substrates after hot dipping and diffusion annealing Proceedings of the Third international conference on Numerical Analysis and its Applications, (399-407)
- Tin-Loi F and Lee Z (2004). Optimal tilt lifting of beams as a min-max problem, Structural and Multidisciplinary Optimization, 26:1-2, (160-168), Online publication date: 1-Jan-2004.
- Vrahatis M, Magoulas G and Plagianakos V (2003). From linear to nonlinear iterative methods, Applied Numerical Mathematics, 45:1, (59-77), Online publication date: 1-Apr-2003.
- Mayne D and Raković S (2003). Optimal Control of Constrained Piecewise Affine Discrete-Time Systems, Computational Optimization and Applications, 25:1-3, (167-191), Online publication date: 20-Mar-2003.
- Qi L, Wu S and Zhou G (2003). Semismooth Newton Methods for Solving Semi-Infinite Programming Problems, Journal of Global Optimization, 27:2-3, (215-232), Online publication date: 1-Nov-2003.
- Computational Optimization and Applications staff (2003). Photo, Biography and Selected Publications of Professor Elijah Polak, Computational Optimization and Applications, 25:1-3, (11-16), Online publication date: 20-Mar-2003.
- Polak E and Royset J (2003). Cutting Sphere Algorithm, Journal of Optimization Theory and Applications, 119:2, (379-385), Online publication date: 1-Nov-2003.
- Polak E, Royset J and Womersley R (2003). Algorithms with Adaptive Smoothing for Finite Minimax Problems, Journal of Optimization Theory and Applications, 119:3, (459-484), Online publication date: 1-Dec-2003.
- Polak E and Royset J (2003). Algorithms for Finite and Semi-Infinite Min---Max---Min Problems Using Adaptive Smoothing Techniques, Journal of Optimization Theory and Applications, 119:3, (421-457), Online publication date: 1-Dec-2003.
- Molchanov I and Zuyev S (2002). Steepest descent algorithms in a space of measures, Statistics and Computing, 12:2, (115-123), Online publication date: 1-Apr-2002.
- Parsopoulos K and Vrahatis M (2002). Recent approaches to global optimization problems through Particle Swarm Optimization, Natural Computing: an international journal, 1:2-3, (235-306), Online publication date: 1-Jun-2002.
- Gasimov R (2002). Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming, Journal of Global Optimization, 24:2, (187-203), Online publication date: 1-Oct-2002.
- Pieraccini S (2002). Hybrid Newton-Type Method for a Class of Semismooth Equations, Journal of Optimization Theory and Applications, 112:2, (381-402), Online publication date: 1-Feb-2002.
- Ögren P and Martin C (2002). Vaccination strategies for epidemics in highly mobile populations, Applied Mathematics and Computation, 127:2-3, (261-276), Online publication date: 15-Apr-2002.
- Zheng Y, Lin Z and Tay D (2001). State-dependent vector hybrid linear and nonlinear ARMA modeling, Circuits, Systems, and Signal Processing, 20:5, (551-574), Online publication date: 1-Sep-2001.
- Xu S (2001). Smoothing Method for Minimax Problems, Computational Optimization and Applications, 20:3, (267-279), Online publication date: 1-Dec-2001.
- Bagirov A and Rubinov A (2001). Global Optimization of Marginal Functions with Applications to Economic Equilibrium, Journal of Global Optimization, 20:3-4, (215-237), Online publication date: 1-Aug-2001.
- Buss S and Fillmore J (2001). Spherical averages and applications to spherical splines and interpolation, ACM Transactions on Graphics, 20:2, (95-126), Online publication date: 1-Apr-2001.
- Vrahatis M, Magoulas G and Plagianakos V (2000). Globally Convergent Modification of the Quickprop Method, Neural Processing Letters, 12:2, (159-170), Online publication date: 1-Oct-2000.
- Kohn W, Brayman V and Ritcey J (2000). Enterprise Dynamics Via Non-Equilibrium Membrane Models, Open Systems & Information Dynamics, 7:4, (327-348), Online publication date: 2-Nov-2000.
- Gonzaga C (2000). Two Facts on the Convergence of the Cauchy Algorithm, Journal of Optimization Theory and Applications, 107:3, (591-600), Online publication date: 1-Dec-2000.
- Polak E, Qi L and Sun D (1999). First-Order Algorithms for Generalized Semi-Infinite Min-Max Problems, Computational Optimization and Applications, 13:1-3, (137-161), Online publication date: 1-Apr-1999.
Index Terms
- Optimization: algorithms and consistent approximations
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