{"responseHeader":{"status":0,"QTime":7,"params":{"q":"{!q.op=AND}id:\"97662\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"file_name_t":"Cohen-Spacetme_Control.pdf","thumb_s":"/01/7e/017e02f3467cc7d8708a1d545a3f90f5e5d0323a.jpg","oldid_t":"compsci 5775","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-04-27T00:00:00Z","file_s":"/ab/bc/abbc6579c59991635ef46c80afa1bf30fa51403f.pdf","title_t":"Page 36","ocr_t":"22 number.) Expanding the ( k + 1 )\"t iteration into a first order Taylor series around the kth iteration: where: From above, using Newton's method: Because fJ)..k = )..k+I - )..k, one can solve for the changes in the state x, and directly for the next set of Lagrange multipliers, )..k+I : This defines a sequence of quadratic subproblems, hence the name Sequential Quadratic Programming, or SQP, also known as Lagrange-Newton equations. Each step performs a minimization of the Lagrangian subject to a linearized set of constraints. A problem may arise if the current guess is far from the solution and the constraints are highly nonlinear. A standard modification to the above procedure views the fJxk as a step direction and minimizes some merit function along a line Xk + akOXk. The merit function might be some weighted sum of the constraint violation and the objective function. This can be used to keep the iteration from moving outside a possible solution region. The generality and efficiency of the SQP procedure makes it a good prospect for use in solving the spacetime problem. The fact that the objective and constraint can be differentiated in symbolic form can be used to reduce the computation for each iteration.","id":97662,"created_tdt":"2016-04-27T00:00:00Z","parent_i":97747,"_version_":1642982591105597440}]},"highlighting":{"97662":{"ocr_t":[]}}}