{"_id":"7jAk6SxGPLELvKmNm","bibbaseid":"shi-jin---engineering-secondorderoptimalityconditionsandreformulationsfornonconvexquadraticallyconstrainedquadraticprogrammingproblems-2014","author_short":["Shi, Z.","Jin, Q.",",Department of Mathematical Sciences, Tsinghua University, Beijing, 100084",",Department of Management Science","Engineering, Z. U."],"bibdata":{"bibtype":"article","type":"article","title":"Second Order Optimality Conditions and Reformulations for Nonconvex Quadratically Constrained Quadratic Programming Problems","volume":"10","issn":"1553-166X","url":"http://aimsciences.org//article/doi/10.3934/jimo.2014.10.871","doi":"10.3934/jimo.2014.10.871","abstract":"In this paper, we present an optimality condition which could determine whether a given KKT solution is globally optimal. This condition is equivalent to determining if the Hessian of the corresponding Largrangian is copositive over a set. To find the corresponding Lagrangian multiplier, two linear conic programming problems are constructed and then relaxed for computational purpose. Under the new condition, we proposed a local search based scheme to find a global optimal solution and showed its effectiveness by three examples.","language":"en","number":"3","urldate":"2022-01-19","journal":"Journal of Industrial & Management Optimization","author":[{"propositions":[],"lastnames":["Shi"],"firstnames":["Ziye"],"suffixes":[]},{"propositions":[],"lastnames":["Jin"],"firstnames":["Qingwei"],"suffixes":[]},{"firstnames":[],"propositions":[],"lastnames":[",Department of Mathematical Sciences, Tsinghua University, Beijing, 100084"],"suffixes":[]},{"firstnames":[],"propositions":[],"lastnames":[",Department of Management Science"],"suffixes":[]},{"propositions":[],"lastnames":["Engineering"],"firstnames":["Zhejiang","University"],"suffixes":["Hangzhou",",","Zhejiang","310058"]}],"year":"2014","keywords":"/unread","pages":"871–882","bibtex":"@article{shi_second_2014,\n\ttitle = {Second {Order} {Optimality} {Conditions} and {Reformulations} for {Nonconvex} {Quadratically} {Constrained} {Quadratic} {Programming} {Problems}},\n\tvolume = {10},\n\tissn = {1553-166X},\n\turl = {http://aimsciences.org//article/doi/10.3934/jimo.2014.10.871},\n\tdoi = {10.3934/jimo.2014.10.871},\n\tabstract = {In this paper, we present an optimality condition which could determine whether a given KKT solution is globally optimal. This condition is equivalent to determining if the Hessian of the corresponding Largrangian is copositive over a set. To find the corresponding Lagrangian multiplier, two linear conic programming problems are constructed and then relaxed for computational purpose. Under the new condition, we proposed a local search based scheme to find a global optimal solution and showed its effectiveness by three examples.},\n\tlanguage = {en},\n\tnumber = {3},\n\turldate = {2022-01-19},\n\tjournal = {Journal of Industrial \\& Management Optimization},\n\tauthor = {Shi, Ziye and Jin, Qingwei and {,Department of Mathematical Sciences, Tsinghua University, Beijing, 100084} and {,Department of Management Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310058}},\n\tyear = {2014},\n\tkeywords = {/unread},\n\tpages = {871--882},\n}\n\n","author_short":["Shi, Z.","Jin, Q.",",Department of Mathematical Sciences, Tsinghua University, Beijing, 100084",",Department of Management Science","Engineering, Z. U."],"key":"shi_second_2014","id":"shi_second_2014","bibbaseid":"shi-jin---engineering-secondorderoptimalityconditionsandreformulationsfornonconvexquadraticallyconstrainedquadraticprogrammingproblems-2014","role":"author","urls":{"Paper":"http://aimsciences.org//article/doi/10.3934/jimo.2014.10.871"},"keyword":["/unread"],"metadata":{"authorlinks":{}},"html":""},"bibtype":"article","biburl":"https://bibbase.org/zotero/victorjhu","dataSources":["CmHEoydhafhbkXXt5"],"keywords":["/unread"],"search_terms":["second","order","optimality","conditions","reformulations","nonconvex","quadratically","constrained","quadratic","programming","problems","shi","jin",",department of mathematical sciences, tsinghua university, beijing, 100084",",department of management science","engineering"],"title":"Second Order Optimality Conditions and Reformulations for Nonconvex Quadratically Constrained Quadratic Programming Problems","year":2014}