메뉴 건너뛰기




Volumn 121, Issue 3, 2004, Pages 541-570

Regularized Lotka-Volterra dynamical system as continuous proximal-like method in optimization

Author keywords

asymptotic analysis; continuous gradient method; Dynamical systems; implicit discrete scheme; interior proximal algorithms; Lotka Volterra differential equations; Lyapunov functions; regularized logarithmic barrier; relative entropy; viability

Indexed keywords

ASYMPTOTIC ANALYSIS; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; GRADIENT METHODS;

EID: 4444249204     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000037603.51578.45     Document Type: Article
Times cited : (29)

References (29)
  • 2
    • 0032169238 scopus 로고    scopus 로고
    • A Dynamical System Associated with Newton's Method for Parametric Approximations of Convex Minimization Problems
    • ALVAREZ, F., and PEREZ, J. M., A Dynamical System Associated with Newton's Method for Parametric Approximations of Convex Minimization Problems, Applied Mathematics and Optimization, Vol. 38, pp. 193-217, 1998.
    • (1998) Applied Mathematics and Optimization , vol.38 , pp. 193-217
    • Alvarez, F.1    Perez, J.M.2
  • 3
    • 0033713021 scopus 로고    scopus 로고
    • On the Minimizing Property of Second-Order Dissipative Systems in Hilbert Spaces
    • ALVAREZ, F., On the Minimizing Property of Second-Order Dissipative Systems in Hilbert Spaces, SIAM Journal on Control and Optimization, Vol. 38, pp. 1102-1119, 2000.
    • (2000) SIAM Journal on Control and Optimization , vol.38 , pp. 1102-1119
    • Alvarez, F.1
  • 4
    • 0010753166 scopus 로고
    • Minimization of Convex Functions on Convex Sets by Means of Differential Equations
    • ANTIPIN, A. S., Minimization of Convex Functions on Convex Sets by Means of Differential Equations, Differential Equations, Vol. 30, pp. 1364-1374, 1994.
    • (1994) Differential Equations , vol.30 , pp. 1364-1374
    • Antipin, A.S.1
  • 5
    • 0030187531 scopus 로고    scopus 로고
    • A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method
    • ATTOUCH, H., and COMINETTI, R., A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method, Journal of Differential Equations, Vol. 128, pp. 519-540, 1996.
    • (1996) Journal of Differential Equations , vol.128 , pp. 519-540
    • Attouch, H.1    Cominetti, R.2
  • 7
    • 0347211612 scopus 로고    scopus 로고
    • An Asymptotical Variational Principle Associated with the Steepest Descent Method for a Convex Function
    • LEMAIRE, B., An Asymptotical Variational Principle Associated with the Steepest Descent Method for a Convex Function, Journal of Convex Analysis, Vol. 3, pp. 63-70, 1996.
    • (1996) Journal of Convex Analysis , vol.3 , pp. 63-70
    • Lemaire, B.1
  • 8
    • 0001725820 scopus 로고
    • Perturbation des Méthodes d'Optimisation: Applications
    • MARTINET, B., Perturbation des Méthodes d'Optimisation: Applications, RAIRO Analyse Numérique, Vol. 12, pp. 153-171, 1978.
    • (1978) RAIRO Analyse Numérique , vol.12 , pp. 153-171
    • Martinet, B.1
  • 9
    • 0016985417 scopus 로고
    • Monotone Operators and the Proximal Point Algorithm
    • ROCKAFELLAR, R. T., Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, Vol. 14, pp. 877-898, 1976.
    • (1976) SIAM Journal on Control and Optimization , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 10
    • 0029207145 scopus 로고
    • An Interior Proximal Method for Convex Linearly Constrained Problems and Its Extension to Variational Inequalities
    • AUSLENDER, A., and HADDOU, M., An Interior Proximal Method for Convex Linearly Constrained Problems and Its Extension to Variational Inequalities, Mathematical Programming, Vol. 71, pp. 77-100, 1995.
    • (1995) Mathematical Programming , vol.71 , pp. 77-100
    • Auslender, A.1    Haddou, M.2
  • 11
    • 0002815417 scopus 로고
    • Multiplicatively Iterative Algorithms for Convex Programming
    • EGGERMONT, P. P. B., Multiplicatively Iterative Algorithms for Convex Programming, Linear Algebra and Its Applications, Vol. 130, pp. 25-42, 1990.
    • (1990) Linear Algebra and Its Applications , vol.130 , pp. 25-42
    • Eggermont, P.P.B.1
  • 13
    • 0001286634 scopus 로고
    • Entropic Proximal Mappings with Application to Nonlinear Programming
    • TEBOULLE, M., Entropic Proximal Mappings with Application to Nonlinear Programming, Mathematics of Operations Research, Vol. 17, pp. 670-690, 1992.
    • (1992) Mathematics of Operations Research , vol.17 , pp. 670-690
    • Teboulle, M.1
  • 14
    • 0031285685 scopus 로고    scopus 로고
    • Convergence of Proximal-Like Algorithms
    • TEBOULLE, M., Convergence of Proximal-Like Algorithms, SIAM Journal on Optimization, Vol. 7, pp. 1069-1083, 1997.
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 1069-1083
    • Teboulle, M.1
  • 16
    • 34249830808 scopus 로고
    • Modified Barrier Functions Theory and Methods
    • POLYAK, R. A., Modified Barrier Functions Theory and Methods, Mathematical Programming, Vol. 54, pp. 177-222, 1992.
    • (1992) Mathematical Programming , vol.54 , pp. 177-222
    • Polyak, R.A.1
  • 17
    • 0041629347 scopus 로고    scopus 로고
    • Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization
    • POLYAK, R. A., and TEBOULLE, M., Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization, Mathematical Programming, Vol. 76, pp. 265-284, 1997.
    • (1997) Mathematical Programming , vol.76 , pp. 265-284
    • Polyak, R.A.1    Teboulle, M.2
  • 18
    • 0027607344 scopus 로고
    • On the Convergence of the Exponential Multiplier Method for Convex Programming
    • TSENG, P., and BERTSEKAS, D., On the Convergence of the Exponential Multiplier Method for Convex Programming, Mathematical Programming, Vol. 60, pp. 1-19, 1993.
    • (1993) Mathematical Programming , vol.60 , pp. 1-19
    • Tseng, P.1    Bertsekas, D.2
  • 19
    • 0031190440 scopus 로고    scopus 로고
    • Proximal Minimization Methods with Generalized Bregman Functions
    • KIWIEL, K. C., Proximal Minimization Methods with Generalized Bregman Functions, SIAM Journal on Control and Optimization, Vol. 35, pp. 1142-1168, 1997.
    • (1997) SIAM Journal on Control and Optimization , vol.35 , pp. 1142-1168
    • Kiwiel, K.C.1
  • 20
    • 0033358882 scopus 로고    scopus 로고
    • Interior Proximal and Multiplier Methods Based on Second-Order Homogeneous Kernels
    • AUSLENDER, A., TEBOULLE, M., and BEN-TIBA, S., Interior Proximal and Multiplier Methods Based on Second-Order Homogeneous Kernels, Mathematics of Operations Research, Vol. 24, pp. 645-668, 1999.
    • (1999) Mathematics of Operations Research , vol.24 , pp. 645-668
    • Auslender, A.1    Teboulle, M.2    Ben-Tiba, S.3
  • 21
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 22
    • 84966258893 scopus 로고
    • The Nonlinear Geometry of Linear Programming: Part I, Affine and Projective Scaling Trajectories, Part II, Legendre Transform Coordinates and Central Trajectories
    • BAYER, D. A., and LAGARIAS, J. C., The Nonlinear Geometry of Linear Programming: Part I, Affine and Projective Scaling Trajectories, Part II, Legendre Transform Coordinates and Central Trajectories, Transactions of the American Mathematical Society, Vol. 314, pp. 499-526, 1989 and Vol. 314, pp. 527-581, 1989.
    • (1989) Transactions of the American Mathematical Society , vol.314 , pp. 499-526
    • Bayer, D.A.1    Lagarias, J.C.2
  • 23
    • 84966218491 scopus 로고
    • BAYER, D. A., and LAGARIAS, J. C., The Nonlinear Geometry of Linear Programming: Part I, Affine and Projective Scaling Trajectories, Part II, Legendre Transform Coordinates and Central Trajectories, Transactions of the American Mathematical Society, Vol. 314, pp. 499-526, 1989 and Vol. 314, pp. 527-581, 1989.
    • (1989) Transactions of the American Mathematical Society , vol.314 , pp. 527-581
  • 25
    • 0002434869 scopus 로고
    • Asymptotic Convergence of Nonlinear Contraction Semigroups in Hilbert Space
    • BRUCK, R. D., Asymptotic Convergence of Nonlinear Contraction Semigroups in Hilbert Space, Journal of Functional Analysis, Vol. 18, pp. 15-26, 1975.
    • (1975) Journal of Functional Analysis , vol.18 , pp. 15-26
    • Bruck, R.D.1
  • 26
    • 84968481460 scopus 로고
    • Weak Convergence of the Sequence of Successive Approximations for Nonexpansive Mappings
    • OPIAL, Z., Weak Convergence of the Sequence of Successive Approximations for Nonexpansive Mappings, Bulletin of the American Mathematical Society, Vol. 73, pp. 591-597 1967.
    • (1967) Bulletin of the American Mathematical Society , vol.73 , pp. 591-597
    • Opial, Z.1
  • 28
    • 0010975559 scopus 로고    scopus 로고
    • Characterizations of Generalized Convexity and Generalized Monotonicity: A Survey
    • CROUZEIX, J. P., Characterizations of Generalized Convexity and Generalized Monotonicity: A Survey, Nonconvex Optimization and Applications, Vol. 27, pp. 237-256, 1998.
    • (1998) Nonconvex Optimization and Applications , vol.27 , pp. 237-256
    • Crouzeix, J.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.