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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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1573-2878

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Stability and Controllability Issues in Mathematic

Authors: L Berezansky S BunimovichMendrazitsky B Shklyar
Publish Date: 2015/02/27
Volume: 167, Issue: 1, Pages: 326-341
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Abstract

We present a mathematical model of dynamic changes in clinical parameters following drug therapy for chronic myeloid leukemia CML using a system of ordinary differential equations ODE describing the interactions between effector T cells and leukemic cancer cells The model successfully predicts clinical response to two separate drug therapies targeted therapy with the tyrosine kinase inhibitor imatinib and immunotherapy with interferon alfa2 Development of this model enables the identification of the treatment regimen for a determined time period in order to reach an admissible concentration of cancer cells To mathematically model the dynamics of CML progression both without and with treatment we have obtained the local and global stability and the local relative controllability conditions for this ODE system

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Other Papers In This Journal:
  1. Incrementally Updated Gradient Methods for Constrained and Regularized Optimization
  2. Periodic Image Trajectories in Earth–Moon Space
  3. On Approximate KKT Condition and its Extension to Continuous Variational Inequalities
  4. A Note on Testing Axioms of Revealed Preference
  5. Duality Theorem for a Three-Phase Partition Problem
  6. Normality and Nondegeneracy for Optimal Control Problems with State Constraints
  7. Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem
  8. The Existence of Optimal Controls for Problems Defined on Time Scales
  9. Annealing a Genetic Algorithm for Constrained Optimization
  10. Convergent Bounds for Stochastic Programs with Expected Value Constraints
  11. Calmness and Exact Penalization in Constrained Scalar Set-Valued Optimization
  12. Splitting Methods with Variable Metric for Kurdyka–Łojasiewicz Functions and General Convergence Rates
  13. On Estimation in Interception Endgames
  14. Studies on Common Solutions of a Variational Inequality and a Fixed-Point Problem
  15. Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type
  16. Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization
  17. Harvesting Control for an Age-Structured Population in a Multilayered Habitat
  18. On Optimization over the Efficient Set in Linear Multicriteria Programming
  19. Some Existence Results of Solutions for General Variational Inequalities
  20. An Algorithm for Portfolio Optimization with Variable Transaction Costs, Part 1: Theory
  21. Sequential gradient-restoration algorithm for optimal control problems with bounded state
  22. Aerial Vehicle Search-Path Optimization: A Novel Method for Emergency Operations
  23. Generalized Qualification and Qualification Levels for Spectral Regularization Methods
  24. Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces
  25. Global Optimality Conditions for Optimal Control Problems with Functions of A.D. Alexandrov
  26. Time-Optimal Control Problem for a Special Class of Control Systems: Optimal Controls and Approximation in the Sense of Time Optimality
  27. Directional Hölder Metric Regularity
  28. Existence and Uniqueness for a Linear Mixed Variational Inequality Arising in Electrical Circuits with Transistors
  29. The Effects of Adding Input Redundancies in Linear Quadratic Regulator Problems
  30. On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations
  31. Synchronization Criterion for Lur’e Systems via Delayed PD Controller
  32. An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions
  33. On an Inequality of C. Sundberg: A Computational Investigation via Nonlinear Programming
  34. Convergence Analysis of Weighted Difference Approximations on Piecewise Uniform Grids to a Class of Singularly Perturbed Functional Differential Equations
  35. Social Interactions within a Dynamic Competitive Economy
  36. Game Analysis of Investment in a Group with Stickiness
  37. SI “Deterministic and Stochastic Variational Principles and Applications”. December 2015
  38. A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds
  39. Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy
  40. Approximate Functions in a Problem of Sets Separation
  41. Feasible Method for Generalized Semi-Infinite Programming
  42. On the Convergence of Adaptive Stochastic Search Methods for Constrained and Multi-objective Black-Box Optimization
  43. Stability of Solutions to Hamilton–Jacobi Equations Under State Constraints
  44. On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions
  45. A Generalization of the Classical α BB Convex Underestimation via Diagonal and Nondiagonal Quadratic Terms
  46. Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method
  47. On the Finite Convergence of a Projected Cutter Method
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