Differential Stochastic Variational Inequalities with Parametric Optimization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915493285199872 |
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| author | Chen, Xiaojun Guo, Jian Wang, Guan |
| author_facet | Chen, Xiaojun Guo, Jian Wang, Guan |
| contents | The differential stochastic variational inequality with parametric convex optimization (DSVI-O) is an ordinary differential equation whose right-hand side involves a stochastic variational inequality and solutions of several dynamic and random parametric convex optimization problems. We consider that the distribution of the random variable is time-dependent and assume that the involved functions are continuous and the expectation is well-defined. We show that the DSVI-O has a weak solution with integrable and measurable solutions of the parametric optimization problems. Moreover, we propose a discrete scheme of DSVI-O by using a time-stepping approximation and the sample average approximation and prove the convergence of the discrete scheme. We illustrate our theoretical results of DSVI-O with applications in an embodied intelligence system for the elderly health by synthetic health care data generated by Multimodal Large Language Models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential Stochastic Variational Inequalities with Parametric Optimization Chen, Xiaojun Guo, Jian Wang, Guan Optimization and Control Dynamical Systems 90C15, 90C33, 90C39 The differential stochastic variational inequality with parametric convex optimization (DSVI-O) is an ordinary differential equation whose right-hand side involves a stochastic variational inequality and solutions of several dynamic and random parametric convex optimization problems. We consider that the distribution of the random variable is time-dependent and assume that the involved functions are continuous and the expectation is well-defined. We show that the DSVI-O has a weak solution with integrable and measurable solutions of the parametric optimization problems. Moreover, we propose a discrete scheme of DSVI-O by using a time-stepping approximation and the sample average approximation and prove the convergence of the discrete scheme. We illustrate our theoretical results of DSVI-O with applications in an embodied intelligence system for the elderly health by synthetic health care data generated by Multimodal Large Language Models. |
| title | Differential Stochastic Variational Inequalities with Parametric Optimization |
| topic | Optimization and Control Dynamical Systems 90C15, 90C33, 90C39 |
| url | https://arxiv.org/abs/2508.15241 |