Research on the descent direction of prediction correction algorithms for pseudo-convex/convex optimization problems

Fuente: arXiv
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Main Authors: Li, Ting, Han, Deren, Wang, Tanxing, Cai, Xingju
Format: Preprint
Published: 2025
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author Li, Ting
Han, Deren
Wang, Tanxing
Cai, Xingju
author_facet Li, Ting
Han, Deren
Wang, Tanxing
Cai, Xingju
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_04575
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Research on the descent direction of prediction correction algorithms for pseudo-convex/convex optimization problems
Li, Ting
Han, Deren
Wang, Tanxing
Cai, Xingju
Optimization and Control
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.
title Research on the descent direction of prediction correction algorithms for pseudo-convex/convex optimization problems
topic Optimization and Control
url https://arxiv.org/abs/2512.04575