What question did this study set out to answer?

To develop a recursive stochastic subgradient framework for solving stochastic programming problems with nonsmooth objective functions and constraints.

February 1, 1987Mathematics of Operations Research

A Linearization Method for Nonsmooth Stochastic Programming Problems

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Authors

ARAndrzej RuszczyńskiRutgers, The State University of New Jersey

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Implication

Theoretical analysis demonstrates almost sure convergence of a recursive subgradient method for nonsmooth stochastic optimization, highlighting reliable identification of optimal stationary points.

Key Points

To develop a recursive stochastic subgradient framework for solving stochastic programming problems with nonsmooth objective functions and constraints.
Formulated iterative search directions using quadratic programming subproblems based on linearized constraints.
Approximated the nonsmooth objective using quadratic functions constructed with dynamically estimated stochastic ϵ-subgradients.
Evaluated stability and asymptotic behavior using a specialized Lyapunov function technique.
Proved that the recursive method converges with probability 1 to stationary points.
Demonstrated reliable recovery of the subgradients and Lagrange multipliers required for first-order optimality conditions.

Cite This Study

Andrzej Ruszczyński (1987) studied this question.

synapsesocial.com/papers/6a1278c2ea48cb855a34eaa1 https://doi.org/10.1287/moor.12.1.32

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Implication

Theoretical analysis demonstrates almost sure convergence of a recursive subgradient method for nonsmooth stochastic optimization, highlighting reliable identification of optimal stationary points.

A Linearization Method for Nonsmooth Stochastic Programming Problems

Discussion

Member takes

Implication

Key Points

Cite This Study

A Linearization Method for Nonsmooth Stochastic Programming Problems

Discussion

Member takes

Implication

Key Points

Cite This Study

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