An algorithm for approximating piecewise linear concave functions from sample gradients

Operations Research Letters

Volumn 31, Issue 1, 2003, Pages 66-76

  Topaloglu, Huseyin ^a   Powell, Warren B ^a  

^a Princeton University   (United States)

Author keywords

Almost sure convergence; Approximation; Concave functions; Stochastic gradient methods

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; RANDOM PROCESSES;

CONCAVE FUNCTIONS;

PROBLEM SOLVING;

EID: 0037211354     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(02)00187-6     Document Type: Article

References (9)

1. Au K., Higle J., Sen S. Inexact subgradient methods with applications in stochastic programming. Math. Programming. 63(1):1994;65-82.
2. Birge J., Qi L. Subdifferential convergence in stochastic systems. SIAM J. Optim. 5(2):1995;436-453.
3. Birge J., Qi L., Wei Z. Convergence analysis of some methods for minimizing a nonsmooth convex function. J. Optim. Theory Appl. 97(2):1998;357-383.
4. Chen Z.-L., Powell W.B. A convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse. J. Optim. Theory Appl. 102(3):1999;497-524.
5. Ermoliev Y. Stochastic quasigradient methods. Ermoliev Y., Wets R. Numerical Techniques for Stochastic Optimization. 1988;Springer, Berlin.
6. Godfrey G.A., Powell W.B. An adaptive, distribution-free approximation for the newsvendor problem with censored demands, with applications to inventory and distribution problems. Manage. Sci. 47(8):2001;1101-1112.
7. Godfrey G., Powell W.B. An adaptive, dynamic programming algorithm for stochastic resource allocation problems. I. single period travel times Transportation Sci. 36(1):2002;21-39.
8. Gupal A.M., Bazhenov L.G. A stochastic method of linearization. Cybernetics. 8:1972;482-484.
9. Higle J., Sen S. Stochastic decomposition. an algorithm for two stage linear programs with recourse Math. Oper. Res. 16(3):1991;650-669.