Xingju Cai

1. Let H be a real Hilbert space equipped with the inner product ⟨⋅,⋅⟩ and the induced norm ‖⋅‖. Let A,C:H→2H be maximal monotone operators, and let B:H→H be a β-cocoercive operator for some β>0. I...

Sampling is a major computational bottleneck in stochastic algorithms. This paper proposes a stochastic projection contraction algorithm for stochastic variational inequality problems, significantly reducing runtime by eliminating resampling in the correction step. We introduce an adjustable offset weight to optimize search direction, along with different adaptive step size strategies in prediction and correction steps. We further present discrete differential equation interpretations for specific offset weight values. To address bias due to the absence of resampling in the correction step, we develop an error control scheme and provide convergence guarantees. Numerical experiments demonstrate the algorithm’s efficiency

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the prediction step. This paper investigates the adjustment coefficients of these descent directions and offers explanations from the perspective of differential equations. Unlike existing algorithms where the adjustment coefficient is always set to 1, we establish that the range of the adjustment coefficient lies within (1/2,1] for pseudo-convex optimization problems, and [0,1] for convex optimization problems. We also provide rigorous convergence proofs for these proposed algorithms. Numerical experiment results show that the algorithms perform best when the value of the adjustment coefficient makes the algorithm approach or equal to those in differential equations with higher-order global discrete error.