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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.20992 |
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| _version_ | 1866917430357393408 |
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| author | Yu, Jiguang |
| author_facet | Yu, Jiguang |
| contents | In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain why it fails in the equilibrium-constrained setting, and develop the three main viewpoints used in the literature: (i) multiplier-based conditions, (ii) implicit-programming conditions based on the solution map of the lower-level equilibrium system, and (iii) piecewise-programming conditions obtained by decomposing complementarity structure into smooth pieces. The emphasis is on conceptual structure, critical cones, strong regularity, and the exact role of curvature terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimization Workshop Notes for Mathematical Programming with Equilibrium Constraints (MPECs): Second-Order Optimality Conditions Yu, Jiguang Optimization and Control In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain why it fails in the equilibrium-constrained setting, and develop the three main viewpoints used in the literature: (i) multiplier-based conditions, (ii) implicit-programming conditions based on the solution map of the lower-level equilibrium system, and (iii) piecewise-programming conditions obtained by decomposing complementarity structure into smooth pieces. The emphasis is on conceptual structure, critical cones, strong regularity, and the exact role of curvature terms. |
| title | Optimization Workshop Notes for Mathematical Programming with Equilibrium Constraints (MPECs): Second-Order Optimality Conditions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.20992 |