{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:23:39Z","timestamp":1787383419851,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>In this paper an algorithm for extracting a stable differential-algebraic subsystem from a path-constrained dynamical system is proposed. The subsystem may be integrated directly by a differential-algebraic system integrator to evaluate constraints in shooting- or multiple shooting-type direct methods for solving path-constrained dynamic optimization problems. The algorithm appends algebraic constraints to the unconstrained ordinary differential equation subsystem based on a stability estimate for the resulting differential-algebraic system. The logarithmic norm is used to compute a stability estimate for index 1 and index 2 subsystems. The working of the algorithm is illustrated with examples.<\/jats:p>","DOI":"10.1137\/s1064827500372390","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"2051-2074","source":"Crossref","is-referenced-by-count":4,"title":["Constraint Partitioning for Stability in Path-Constrained Dynamic Optimization Problems"],"prefix":"10.1137","volume":"22","author":[{"given":"Soumyendu","family":"Raha","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linda R.","family":"Petzold","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971392"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971231"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0914007"},{"key":"R4","unstructured":"J. T. Betts,\n                      Exploiting sparsity in the direct transcription method for optimal control point to point path optimization\n                      , in Proceedings of the International Symposium on Mathematical Programming, EPFL, Lausanne, Switzerland, 1997."},{"key":"R5","volume-title":"Numerical solution of initial\u2010value problems in differential\u2010algebraic equations","author":"Brenan K.","year":"1996"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1080\/08905459508905235"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690440505"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899353622"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0607066"},{"key":"R10","unstructured":"W. F. Feehery, J. R. Banga, and P. I. Barton,\n                      A novel approach to dynamic optimization of ODE and DAE systems as high index problems\n                      , in Proceedings of the AIChE Annual Meeting, Miami Beach, FL, 1995."},{"key":"R11","volume-title":"Solving ordinary differential equations. I","author":"Hairer E.","year":"1993"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09947-6"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0093947"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01989751"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00464-7"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00310-1"},{"key":"R17","unstructured":"S. Raha and L. R. Petzold,\n                      Constraint partitioning for structure in path\u2010constrained dynamic optimization problems\n                      , Appl. Numer. 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