{"responseHeader":{"status":0,"QTime":7,"params":{"q":"{!q.op=AND}id:\"97679\"","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":"/01/9a/019acd6e47586351e0ccc4bdbb48e53d3f69de33.jpg","oldid_t":"compsci 5792","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-04-27T00:00:00Z","file_s":"/53/8e/538e1d7836655fbab294547b0d7bdfe062182732.pdf","title_t":"Page 53","ocr_t":"39 containing only y will lead to the same result. Unfortunately this is not true in the general case. Consider the objective: f(x, y) = 5x2 + 6xy + 5y2 This rotated stretched paraboloid cannot be optimized by considering x and y independently; thus, an iterative solution performed on x and then on y will be very sensitive to the starting values given. In fact any function for which the Hessian contains nonzero off diagonal terms will have this property. This does not immediately mean that the problem cannot be separated. The eigenvectors of the Hessian [~0 160] are ( v'2/2, -v'2/2) and ( V2/2, v'2/2), thus a 45 degree rotation of the coordinate system will provide a new system in which the problem is separable. In some cases such a change of coordinates can be used; however, in general, this strategy either cannot be used or is difficult to implement. There may, however, still be some computational .advantage in using an iterative windowing strategy, i.e., optimize in x, then in y, and then repeat. In fact, most iterative strategies adopt a similar scheme of selecting a search \"direction\" (usually determined by some function of the local gradient of the objective), minimizing along such a line, and then determining a new direction to search. Consider the objective (that also has the same eigenvectors): f(x, y) = 100x2 + xy + 100y2 Although this objective cannot strictly be optimized by considering x and y independently, the fact that the Hessian [ 2010 1 ] 200","id":97679,"created_tdt":"2016-04-27T00:00:00Z","parent_i":97747,"_version_":1642982591110840322}]},"highlighting":{"97679":{"ocr_t":[]}}}