[ojAlgo-user] "Approximate" optimization results that don't satisfy constraints

[Edward T. <et...@gm...>]

Hello,

I am investigating ojalgo in the context of portfolio/investment
optimization.  Unlike the typical Markowitz case, our use case contains
real-world complications including shorting assets, transaction costs, and
limiting gross and net exposure.  The problem can still be modeled as a
quadratic optimization, but the number of variables increases quite a bit.
 I was gradually increasing the number of variables into ojalgo and got
stopped pretty quickly.  At around 200 variables I receive results that are
"Approximate" and in fact the result provided did not match the simple
constraints of the problem.  I found this quite strange as finding a
solution matching the constraints is very simple (and such a starting point
was provided to the optimizer).  Why would the optimizer return me an
"Approximate" solution that doesn't match the constraints at all rather
than returning me the best solution meeting the constraints that it could
find (including the one I provided as the starting point)?

The problem as I'm currently setting it up is relatively straightforward
other than the large-ish number of variables.  Each variable has a min and
max constraint, which are the only constraints I'm providing so far.  The
objective is then a standard quadratic objective to be minimized.

I'm setting up the problem by constructing an ExpressionsBasedModel,
providing it the variables (each with a lower, upper, and starting value),
and then providing the model the quadratic and linear expressions to be
minimized.

Any feedback or assistance would be appreciated.

Here is a toString of the model after being minimized in case it helps.
 You can see that most of the variables are wildly outside of their bounds.

############################################
0.000047 <= v0: 0.000047 <= 0.002593
0 <= v1: 12.399095 <= 0.002180
-0.002822 <= v2: -1.639345 <= 0
-0.002617 <= v3: 9.242242 <= 0
-0.002228 <= v4: -6.685084 <= 0
-0.002006 <= v5: 7.002208 <= 0
0.000099 <= v6: 0.001492 <= 0.001492
0 <= v7: -15.831819 <= 0.001120
0.000154 <= v8: -0.654343 <= 0.004867
0 <= v9: -0.654343 <= 0.003971
0.000004 <= v10: 0.004626 <= 0.004626
0 <= v11: -3.352390 <= 0.004041
0 <= v12: 10.393662 <= 0.003149
0 <= v13: 10.393662 <= 0.002781
-0.002782 <= v14: -0.002782 <= -0.000033
-0.002372 <= v15: 14.427516 <= 0
-0.013213 <= v16: -0.013213 <= -0.000521
-0.010585 <= v17: -19.335598 <= 0
-0.002088 <= v18: -9.886252 <= 0
-0.001852 <= v19: 7.130217 <= 0
0.000840 <= v20: 0.000840 <= 0.009390
0 <= v21: 24.037796 <= 0.006642
0.000016 <= v22: -3.275853 <= 0.002073
0 <= v23: -3.275853 <= 0.001784
0 <= v24: -0.926375 <= 0.002628
0 <= v25: -0.926375 <= 0.002318
0.000014 <= v26: 4.944956 <= 0.002697
0 <= v27: 4.944956 <= 0.002334
0.000727 <= v28: -0.801618 <= 0.007707
0 <= v29: -0.801618 <= 0.005381
0.000168 <= v30: 0.000168 <= 0.006497
0 <= v31: 0 <= 0.005370
-0.003646 <= v32: -0.000007 <= -0.000007
-0.003178 <= v33: -9.548069 <= 0
-0.006960 <= v34: -30.222010 <= 0
-0.006120 <= v35: 9.120492 <= 0
-0.002726 <= v36: -0.002726 <= -0.000039
-0.002313 <= v37: 10.738876 <= 0
0 <= v38: 15.791419 <= 0.006325
0 <= v39: 15.791419 <= 0.005569
-0.003546 <= v40: -0.000007 <= -0.000007
-0.003090 <= v41: 10.877754 <= 0
0.000017 <= v42: 0.001999 <= 0.001999
0 <= v43: -12.511306 <= 0.001718
0.000172 <= v44: 0.000172 <= 0.010036
0 <= v45: 11.863053 <= 0.008460
0.000116 <= v46: -0.196284 <= 0.005268
0 <= v47: -0.196284 <= 0.004392
0.000310 <= v48: 1.026073 <= 0.004785
0 <= v49: 1.026073 <= 0.003606
0.000027 <= v50: 0.003538 <= 0.003538
0 <= v51: -13.694850 <= 0.003045
0.000314 <= v52: -2.658083 <= 0.012414
0 <= v53: -2.658083 <= 0.010274
0.000031 <= v54: 0.007608 <= 0.007608
0 <= v55: 3.578124 <= 0.006599
0 <= v56: 5.966903 <= 0.004941
0 <= v57: 5.966903 <= 0.004518
0 <= v58: -10.980529 <= 0.019227
-0.019227 <= v59: 8.256236 <= 0
-0.008174 <= v60: -22.822929 <= 0
-0.007344 <= v61: 8.710203 <= 0
0 <= v62: 5.836502 <= 0.001974
0 <= v63: 5.836502 <= 0.001759
0 <= v64: -31.361763 <= 0.001513
-0.001513 <= v65: 38.911668 <= 0
-0.005145 <= v66: -13.969862 <= 0
-0.004651 <= v67: 8.621640 <= 0
0.000003 <= v68: 0.007058 <= 0.007058
0 <= v69: -23.345131 <= 0.006170
-0.009407 <= v70: -9.911777 <= 0
-0.008307 <= v71: -2.999295 <= 0
0 <= v72: -6.330518 <= 0.006093
0 <= v73: -6.330518 <= 0.005362
0.000024 <= v74: 0.001785 <= 0.001785
0 <= v75: -24.557506 <= 0.001516
-0.002806 <= v76: -0.002806 <= -0.000017
-0.002424 <= v77: 25.120967 <= 0
-0.004065 <= v78: -12.482007 <= 0
-0.003562 <= v79: 18.072430 <= 0
0.000014 <= v80: 7.902697 <= 0.001913
0 <= v81: 7.902697 <= 0.001647
-0.004862 <= v82: -23.278184 <= 0
-0.004341 <= v83: 15.855152 <= 0
-0.003301 <= v84: -7.672005 <= -0.000074
-0.002750 <= v85: 4.081453 <= 0
-0.011429 <= v86: -9.231121 <= 0
-0.010169 <= v87: 20.433090 <= 0
0.000044 <= v88: 0.003628 <= 0.003628
0 <= v89: -20.725597 <= 0.003091
-0.003857 <= v90: -8.605115 <= 0
-0.003523 <= v91: 4.038718 <= 0
0 <= v92: -3.002273 <= 0.006223
-0.006223 <= v93: 40.654612 <= 0
-0.004187 <= v94: -0.004187 <= -0.000001
-0.003662 <= v95: 2.308138 <= 0
-0.005387 <= v96: -50.121281 <= 0
-0.005080 <= v97: 6.731258 <= 0
-0.005095 <= v98: -8.260419 <= -0.000143
-0.004190 <= v99: 2.691277 <= 0
-0.004629 <= v100: -20.052445 <= 0
-0.004078 <= v101: 6.520501 <= 0
-0.002092 <= v102: -6.164178 <= 0
-0.001843 <= v103: 36.442212 <= 0
-0.001778 <= v104: -0.001778 <= -0.000071
-0.001423 <= v105: 9.796041 <= 0
-0.008854 <= v106: 4.812977 <= 0
0 <= v107: 4.812977 <= 0.002873
-0.011727 <= v108: 12.051375 <= 0
-0.002280 <= v109: -0.002280 <= -0.000027
-0.001945 <= v110: 11.204495 <= 0
0 <= v111: -9.731284 <= 0.010427
0 <= v112: -9.731284 <= 0.009155
-0.004582 <= v113: -0.004582 <= -0.000051
-0.003913 <= v114: 17.815327 <= 0
0 <= v115: -0.268223 <= 0.001641
0 <= v116: -0.268223 <= 0.001472
0.000177 <= v117: -2.271096 <= 0.002321
0 <= v118: -2.271096 <= 0.001699
-0.003382 <= v119: -0.000008 <= -0.000008
-0.002945 <= v120: -11.239441 <= 0
-0.001377 <= v121: -11.528363 <= 0
-0.001250 <= v122: -3.873247 <= 0
0.000077 <= v123: 2.934028 <= 0.003083
0 <= v124: 2.934028 <= 0.002552
0 <= v125: 14.661636 <= 0.003678
0 <= v126: 14.661636 <= 0.003312
0.000042 <= v127: -1.802925 <= 0.006800
0 <= v128: -1.802925 <= 0.005871
0 <= v129: 11.250457 <= 0.002385
0 <= v130: 11.250457 <= 0.002122
0.000008 <= v131: 0.002320 <= 0.002320
0 <= v132: -10.798308 <= 0.002015
-0.002007 <= v133: -15.310603 <= -0.000087
-0.001592 <= v134: 3.336150 <= 0
0 <= v135: -13.208688 <= 0.004539
0 <= v136: -13.208688 <= 0.004055
0.000004 <= v137: 0.000004 <= 0.002534
0 <= v138: 14.884312 <= 0.002211
-0.003423 <= v139: -4.819391 <= 0
-0.003064 <= v140: 7.298642 <= 0
-0.011636 <= v141: -24.667288 <= 0
0 <= v142: 0 <= 0.000553
-0.011218 <= v143: 9.120121 <= 0
0.000007 <= v144: 0.000007 <= 0.006453
0 <= v145: 8.706559 <= 0.005633
0.000011 <= v146: 0.000011 <= 0.002405
0 <= v147: 5.452150 <= 0.002083
-0.007417 <= v148: -0.000105 <= -0.000105
-0.006293 <= v149: -4.366268 <= 0
0.000015 <= v150: 0.002860 <= 0.002860
0 <= v151: -8.083382 <= 0.002475
-0.004296 <= v152: -12.277851 <= 0
-0.003764 <= v153: 8.536914 <= 0
0 <= v154: -1.525872 <= 0.000283
0 <= v155: -1.525872 <= 0.009001
-0.008718 <= v156: 3.101125 <= 0
0.000272 <= v157: 3.384421 <= 0.007179
0 <= v158: 3.384421 <= 0.005772
-0.011396 <= v159: -5.275025 <= -0.000223
-0.009553 <= v160: 5.121074 <= 0
-0.005891 <= v161: -5.439854 <= -0.000071
-0.005021 <= v162: 3.615476 <= 0
0 <= v163: -3.953251 <= 0.003710
0 <= v164: -3.953251 <= 0.003428
-0.002616 <= v165: -30.472951 <= 0
-0.002310 <= v166: -12.734294 <= 0
-0.003079 <= v167: -0.003079 <= -0.000012
-0.002671 <= v168: 36.036856 <= 0
-0.002525 <= v169: 4.658318 <= 0
-0.002276 <= v170: 23.741247 <= 0
-0.004125 <= v171: -0.004125 <= -0.000030
-0.003554 <= v172: -4.883884 <= 0
-0.004381 <= v173: -27.223216 <= 0
-0.003908 <= v174: 0.373790 <= 0
-0.002665 <= v175: -10.326246 <= 0
-0.002350 <= v176: 20.589187 <= 0
0.000129 <= v177: 3.901199 <= 0.002780
0 <= v178: 3.901199 <= 0.002191
0 <= v179: 4.868897 <= 0.001489
0 <= v180: 4.868897 <= 0.001310
0 <= v181: -2.307442 <= 0.003723
0 <= v182: -2.307442 <= 0.003519
secondOrderMinimization: 0.766253 (1.000000)
linearMinimization: -1.532517 (1.000000)
############################################