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This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal method of multipliers, to solve this convex stochastic optimization problem. This algorithm can be roughly viewed as a hybrid of stochastic approximation and the traditional proximal method of multipliers. Under mild conditions, we show that this algorithm exhibits $O(K^{-1/2})$ expected convergence rates for both objective reduction and constraint violation if parameters in the algorithm are properly chosen, where $K$ denotes the number of iterations. Moreover, we show that, with high probability, the algorithm has $O(log(K)K^{-1/2})$ constraint violation bound and $O(log^{3/2}(K)K^{-1/2})$ objective bound. Some preliminary numerical results demonstrate the performance of the proposed algorithm.
This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation type algorithm, namely the stochastic ap
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new stochastic
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined wit
We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to advances in
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic optimization proble