{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T04:43:09Z","timestamp":1766983389242,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T00:00:00Z","timestamp":1745884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801381","11901422","JYTMS20230279"],"award-info":[{"award-number":["11801381","11901422","JYTMS20230279"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801381","11901422","JYTMS20230279"],"award-info":[{"award-number":["11801381","11901422","JYTMS20230279"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Liaoning Provincial Department of Education","award":["11801381","11901422","JYTMS20230279"],"award-info":[{"award-number":["11801381","11901422","JYTMS20230279"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the optimality conditions and perform a stability analysis for the second-order cone constrained variational inequalities (SOCCVI) problem. The Lagrange function and Karush\u2013Kuhn\u2013Tucker (KKT) condition of the SOCCVI problem is given, and the optimality conditions for the SOCCVI problem are studied. Then, the second-order sufficient condition satisfying the constrained nondegenerate condition is proved. The strong second-order sufficient condition is defined. And the nonsingularity of Clarke\u2019s generalized Jacobian of the KKT point, the strong regularity of the KKT point, the uniform second-order growth condition, the strong stability of the KKT point, and the local Lipschtiz homeomorphism of the KKT point for the SOCCVI problem are proved to be equivalent to each other. Then, the stability theorem of the SOCCVI problem is obtained.<\/jats:p>","DOI":"10.3390\/axioms14050342","type":"journal-article","created":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T11:00:54Z","timestamp":1745924454000},"page":"342","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimality Conditions and Stability Analysis for the Second-Order Cone Constrained Variational Inequalities"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8414-1454","authenticated-orcid":false,"given":"Li","family":"Wang","sequence":"first","affiliation":[{"name":"School of Science, Shenyang Aerospace University, Shenyang 110136, China"}]},{"given":"Yining","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Science, Shenyang Aerospace University, Shenyang 110136, China"}]},{"given":"Juhe","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Science, Shenyang Aerospace University, Shenyang 110136, China"}]},{"given":"Yanhong","family":"Yuan","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"Geophysical Research Institute, SINOPEC Shengli Oilfield Company, Dongying 257022, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2250030","DOI":"10.1142\/S0217595922500300","article-title":"An implementable augmented Lagrangian method for solving second-order cone constrained variational inequalities","volume":"40","author":"Sun","year":"2023","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/j.cam.2018.08.030","article-title":"A novel gradient-based neural network for solving convex second-order cone constrained variational inequality problems","volume":"347","author":"Nazemi","year":"2018","journal-title":"J. Comput. Appl. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/0952813X.2019.1647559","article-title":"A new neural network framework for solving convex second-order cone constrained variational inequality problems with an application in multi-finger robot hands","volume":"32","author":"Nazemi","year":"2020","journal-title":"J. Exp. Theor. Artif."},{"key":"ref_4","first-page":"468","article-title":"Note on parametric linear programming","volume":"4","author":"Manne","year":"1953","journal-title":"RRAND-Corp. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Danskin, J.M. (1967). The Theory of Max-Min and Its Application to Weapons Allocation Problems, Springer.","DOI":"10.1007\/978-3-642-46092-0"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10107-005-0613-4","article-title":"Perturbation analysis of second-order cone programming problems","volume":"104","author":"Bonnans","year":"2005","journal-title":"Math. Prog."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s00186-008-0241-x","article-title":"Properties of equation reformulation of the karush-kuhn-tucker condition for nonl-inear second order cone optimization problems","volume":"70","author":"Wang","year":"2009","journal-title":"Math. Methods Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mosco, U. (1976). Implicit Variational Problems and Quasi-Variational Inequalities, Springer. Lecture Note in Mathematics.","DOI":"10.1007\/BFb0079943"},{"key":"ref_9","unstructured":"Goebel, K., and Reich, S. (1984). Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Faraut, U., and Kor\u00e1nyi, A. (1994). Analysison Symmetric Cones, Oxford University Press. Oxford Mathematical Monographs.","DOI":"10.1093\/oso\/9780198534778.001.0001"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1023\/A:1022996819381","article-title":"Complementarity Functions and Numerical Experiments for Second-Order-Cone Complementarity Problems","volume":"25","author":"Chen","year":"2003","journal-title":"J. Comput. Optim. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1007\/s11228-008-0092-x","article-title":"On the coderivative of the projection operator onto the second order cone","volume":"16","author":"Outrata","year":"2008","journal-title":"Set-Valued Anal."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T., and Wets, R.J.-B. (1998). Variational Analysis, Springer.","DOI":"10.1007\/978-3-642-02431-3"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bonnans, J.F., and Shapiro, A. (2000). Perturbation Analysis of Optimization Problems, Springer.","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s10107-005-0577-4","article-title":"Strong semismoothness of the Fischer-Burmeister SDC and SOC complementarity functions","volume":"103","author":"Sun","year":"2005","journal-title":"Math. Prog. Ser. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","article-title":"Second-order cone programming","volume":"95","author":"Alizadeh","year":"2003","journal-title":"Math. Prog. Ser. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s11425-009-0207-3","article-title":"Nonsingularity in second-order cone programming via the smoothing metric projector","volume":"53","author":"Wang","year":"2010","journal-title":"Sci. China Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1287\/moor.28.1.39.14258","article-title":"Semismooth homeomorphisms and strong stability of semidefinite and Lorentz cone complementarity problems","volume":"28","author":"Pang","year":"2003","journal-title":"Math. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2140\/pjm.1976.64.97","article-title":"On the inverse function theorem","volume":"64","author":"Clarke","year":"1976","journal-title":"Pac. J. Math."},{"key":"ref_20","unstructured":"Clarke, F.H. (1983). Optimization and Nonsmooth Analysis, John Wiley and Sons."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103547","DOI":"10.1016\/j.compgeo.2020.103547","article-title":"A smoothed finite element method using second-order cone programming","volume":"123","author":"Meng","year":"2020","journal-title":"Comput. Geotech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"112848","DOI":"10.1016\/j.ijsolstr.2024.112848","article-title":"Large deformation of cable networks with fiber sliding as a second-order cone programming","volume":"298","author":"Tkachuk","year":"2024","journal-title":"Int. J. Solids Struct."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/342\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:24:19Z","timestamp":1760030659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/342"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,29]]},"references-count":22,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050342"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050342","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,4,29]]}}}