Thank you for reading my post and or the suggestion. I've attached the trace file as well as a more detailed one. FWIW, to show how similar the solution values are, here is the alglib solution. Please excuse the many decimal places. I generally ignore Visual Studio C++ numerical places beyond 1e13 but I value extreme precision in my problem. Alglib filter sqp: UnitCanonical Ellipsoid 1: (0.329176838420615, 0.94401746027854, 0.0217633576606146) UnitCanonical Ellipsoid 2: (0.930895021061298, 0.329232641233283, 0.158241359036905) In general space, this corresponds to General Ellipsoid 1: (10.5967582185939, 206.347913283321, 6.77869831250489) General Ellipsoid 2: (18.8893523034911, 49.9697297257856, 570.805604711329) The Euclidean norm is: 620.237467405261 In code, of the 6 KKT condition equations, the worst feasibility is 9.7502106655156240e06 and in my Excel "implementation" of my geometric convergence algorithm, the KKT feasibility evaluates as 0.0001294260728173 or roughly 1e4.
In contrast, the point I find in my Excel "algorithm" differs from the ALGLIB solution by at most e9 in unitcanonical space and e8 in general space! My solution: UnitCanonical Ellipsoid 1: (0.32917684136241, 0.944017459191415, 0.0217633603207913) UnitCanonical Ellipsoid 2: (0.930895019622935, 0.329232643072075, 0.158241363672689) In general space, this corresponds to General Ellipsoid 1: (10.5967582026675, 206.347913213863, 6.77869828010731) General Ellipsoid 2: (18.8893522318179, 49.9697297427802, 570.805604707352) The Euclidean norm is: 620.237467405261 In code, of the 6 KKT condition equations, the worst feasibility is 9.0949470177292824e12 and in my Excel "implementation" of my geometric convergence algorithm, the KKT feasibility evaluates as 0.00000000003547029 or roughly 3.5e11.
Does this give you any hints? I realize it may seem like polishing an already very nice apple, but I'd love to squeeze out the extra accuracy from alglib if at all possible...
Attachments: 
File comment: trace_file("SQP.DETAILED,SQP.PROBING,PREC.F15", logDirectory + "trace.log");
trace_15.log [168.53 KiB]
Downloaded 1237 times

File comment: trace_file("SQP", logDirectory + "trace.log");
trace.log [47.92 KiB]
Downloaded 1309 times

