Conjugate gradient type methods for the nondifferentiable convex minimization

Springer Science and Business Media LLC - Tập 7 Số 3 - Trang 533-545 - 2013
Qiong Li1
1College of Mathematics and Econometrics, Hunan University, Changsha, China

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Tài liệu tham khảo

Auslender A.: Numerical methods for nondifferentiable convex optimization. Math. Program. Study 30, 102–126 (1987)

Bagirov A.M., Ganjehlou A.N.: A quasisecant method for minimizing nonsmooth functions. Optim. Methods Softw. 25(1), 3–18 (2009)

Bagirov, A.M., Ganjehlou, A.N.: A secant method for nonsmooth optimization (2009, submitted)

Bagirov A.M., Karasozen B., Sezer M.: Discrete gradient method: a derivative free method for nonsmooth optimization. J. Optim. Theory Appl. 137, 317–334 (2008)

Bonnans J.F., Gilbert J.C., Lemarechal C., Sagastizabal C.: A family of variable-metric proximal methods. Math. Program. 68, 15–47 (1995)

Burke J.V., Qian M.: On the superlinear convergence of the variable—metric proximal point- algorithm using Broyden and BFGS matrix secant updating. Math. Program. 88, 157–181 (2000)

Burke I.V., Lewis A.S.: The speed of Shor’s r-algorithm. IMA J. Numer. Anal. 28, 711–720 (2008)

Cheng W.Y.: A two term PRP based descent method. Numer. Funct. Anal. Optim. 28, 1217–1230 (2007)

Chen X., Fukushima M.: Proximal quasi-Newton methods for nondifferentiable convex optimization. Math. Program. 85, 313–334 (1999)

Correa R., Lemarechal C.: Convergence of some algorithms for convex minimization. Math. Program. 62, 261–275 (1993)

Dai Z., Tian B.: Global convergence of some modified PRP nonlinear conjugate gradient methods. Optim. Lett. 5(4), 615–630 (2011)

Floudas C.A., Pardalos P.M.: Encyclopedia of Optimization. Springer, Berlin (2009)

Fukushima M.: A descent algorithm for nonsmooth convex optimization. Math. Program. 30, 163–175 (1984)

Fukushima M., Qi L.: A globally and superlinearly convergent algorithm for nonsmooth convex minimization. SIAM J. Optim. 6, 1106–1120 (1996)

Hager W.W., Zhang H.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16, 170–192 (2005)

Hager W.W., Zhang H.: A survey of nonlinear conjugate gradient methods. Pac. J. Optim. 2, 35–58 (2006)

Hiriart-Urruty J.-B., Lemarechal C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1993)

Haarala N., Miettinen K., Mäkelä M.M.: Globally convergent limited memory bundle method for large-scale nonsmooth optimization. Math. Program. 109(1), 181–205 (2007)

Kappel F., Kuntsevich A.: An implementation of Shor’s r-algorithm. Comput. Optim. Appl. 15, 193–205 (2005)

Lemarechal, C., Sagastizabal, C.: An approach to variable-metric bundle methods. In: Henry, J., Yuvor, J.P. (eds.) Proceedings of the 16th IFIP-TC7 Conference on Systems Modelling and Optimization, pp. 144–162. Springer, New York (1994)

Lemarechal C., Sagastizabal C.: Practical aspects of the Moreau–Yosida regularization, I: theoretical preliminaries. SIAM J. Optim. 7, 367–385 (1997)

Lu, S., Wei, Z., Li, L.: A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization. Comput. Optim. Appl. (2010, published online)

Lukšan L., Vlček J.: A bundle-Newton method for nonsmooth unconstrained minimization. Math. Program. 83, 373–391 (1998)

Mifflin R.: A quasi-second-order proximal bundle algorithm. Math. Program. 73, 51–72 (1996)

Mifflin R., Sun D., Qi L.: Quasi-Newton bundle-type methods for nondifferentiable convex optimization. SIAM J. Optim. 8, 583–603 (1998)

Mäkelä M.M., Neittaanmäki P.: Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control. World Scientific Publishing Co., Singapore (1992)

Moreau J.J., Panagiotopoulos P.D., Strang G.: Topics in Nonsmooth Mechanics. Birkhäuser Verlag, Basel (1988)

Nesterov YU.: Excessive gap technique in nonsmooth convex minimization. SIAM J. Optim. 16(1), 235–249 (2005)

Nesterov YU.: Smooth minimization of nonsmooth functions. Math. Program. Ser. A 103, 127–152 (2005)

Outrata J., Kočvara M., Zowe J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Theory, Applications and Numerical Results. Kluwer, Dordrecht (1998)

Pardalos P.M., Rassias T.M., Khan A.A.: Nonlinear Analysis and Variational Problems. Springer, Berlin (2010)

Qi L., Chen X.: A preconditioned proximal Newton method for nondifferentiable convex optimization. Math. Program. 76, 411–429 (1997)

Rauf A.I., Fukushima M.: Global convergent BFGS method for nonsmooth convex optimization. J. Optim. Theory Appl. 104(3), 539–558 (2000)

Sagara N., Fukushima M.: A trust region method for nonsmooth convex optimization. J. Ind. Manag. Optim. 1(2), 171–180 (2005)

Shor N.Z.: Minimization Methods for Non-Differentiable Functions. Springer, Berlin (1985)

Yu J., Vishwanathan S.V.N., Günter S., Schraudolph N.N.: A quasi-Newton approach to nonsmooth convex optimization in machine learning. J. Mach. Learn. Res. 11, 1145–1200 (2010)

Zhang L., Zhou W.J., Li D.H.: A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence. IMA J. Numer. Anal. 26, 629–640 (2006)

Zhang L.: A new trust region algorithm for nonsmooth convex minimization. Appl. Math. Comput. 193, 135–142 (2007)