ojalgo - ojalgo BUG：在 ojAlgo 中使用 ConvexSolver 时约束打破权重

Question

我想计算给定协方差矩阵和预期收益的等式和不等式约束的有效边界。这样做时，求解器计算的权重不幸地似乎打破了约束。总体风险和回报似乎还不错。

Primitive64Store tmpCOV = Primitive64Store.FACTORY.rows(new double[][]
{{0.04161599999999999,0.029532687342839998,0.027204649602,0.0077310803303999994,-1.1671155792E-4,-5.6919104880000004E-5,0.011540367260999999,-0.0011583596544,0.0016547567508,0.011887951467599998,-0.0021016779250799997,0.01217717900784,0.0354566417292},
{0.029532687342839998,0.034969,0.02882914496033,0.00673688572095,-1.5753286164E-4,-7.799020878E-5,0.008590460804089999,-0.00120903466574,0.0014109339056999999,0.0104683749489,-0.00296095338671,0.0075381371219,0.03405788034132},
{0.027204649602,0.02882914496033,0.028561000000000003,0.0095923333779,-1.4991438384E-4,-8.476063180000002E-5,0.009686536403049999,-0.0011563569438200001,9.994519899E-4,0.0082659675852,-3.1685615143000007E-4,0.00860292214782,0.03129653885267},
{0.0077310803303999994,0.00673688572095,0.0095923333779,0.011024999999999998,-5.7071784E-6,-1.6705374000000003E-5,0.0062936927109,-2.7820294949999996E-4,8.405088299999999E-5,6.61814874E-4,0.0037795989147,0.0055210432431,0.00810029447955},
{-1.1671155792E-4,-1.5753286164E-4,-1.4991438384E-4,-5.7071784E-6,1.6E-5,5.40282216E-6,-3.1099949760000004E-5,1.671549776E-5,-3.051312E-7,-7.517952359999999E-5,3.06077038E-5,1.3556312E-7,-2.345551502E-4},
{-5.6919104880000004E-5,-7.799020878E-5,-8.476063180000002E-5,-1.6705374000000003E-5,5.40282216E-6,4.0E-6,-1.7530565920000003E-5,3.13729976E-6,-4.841874E-6,-4.2240274199999995E-5,5.2011296E-6,3.44228808E-6,-1.3104418078000002E-4},
{0.011540367260999999,0.008590460804089999,0.009686536403049999,0.0062936927109,-3.1099949760000004E-5,-1.7530565920000003E-5,0.011881,4.4589363133999997E-4,9.499062894E-4,0.0036563291469,0.00251147898767,0.004586606807859999,0.0108024647181},
{-0.0011583596544,-0.00120903466574,-0.0011563569438200001,-2.7820294949999996E-4,1.671549776E-5,3.13729976E-6,4.4589363133999997E-4,0.001444,6.672796998E-4,-9.37965438E-5,0.00112122563298,-0.0011028714312,-0.0013360677697000002},
{0.0016547567508,0.0014109339056999999,9.994519899E-4,8.405088299999999E-5,-3.051312E-7,-4.841874E-6,9.499062894E-4,6.672796998E-4,9.0E-4,0.0013451552549999999,2.136913209E-4,4.8565227479999997E-4,0.0022035050261999998},
{0.011887951467599998,0.0104683749489,0.0082659675852,6.61814874E-4,-7.517952359999999E-5,-4.2240274199999995E-5,0.0036563291469,-9.37965438E-5,0.0013451552549999999,0.0081,-0.0018377539344,0.0026756272619999997,0.0138893569515},
{-0.0021016779250799997,-0.00296095338671,-3.1685615143000007E-4,0.0037795989147,3.06077038E-5,5.2011296E-6,0.00251147898767,0.00112122563298,2.136913209E-4,-0.0018377539344,0.004489000000000001,1.718834348E-4,-0.0025610649546900003},
{0.01217717900784,0.0075381371219,0.00860292214782,0.0055210432431,1.3556312E-7,3.44228808E-6,0.004586606807859999,-0.0011028714312,4.8565227479999997E-4,0.0026756272619999997,1.718834348E-4,0.023716,0.010939810005740002},
{0.0354566417292,0.03405788034132,0.03129653885267,0.00810029447955,-2.345551502E-4,-1.3104418078000002E-4,0.0108024647181,-0.0013360677697000002,0.0022035050261999998,0.0138893569515,-0.0025610649546900003,0.010939810005740002,0.051529000000000005}});


Primitive64Store tmpR =  Primitive64Store.FACTORY.rows(new double[][] {{0.067},{0.045},{0.049},{0.01},{0.02},{1.0E-4},{0.034},{0.001},{0.006},{0.027},{0.005},{0.02},{0.04}});


Primitive64Store tmpEqualityMatrix = Primitive64Store.FACTORY.rows(new double[][]{{1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0}});

Primitive64Store tmpEqualityVector = Primitive64Store.FACTORY.rows(new double[][] {{1}});

Primitive64Store tmpInequalityMatrix = Primitive64Store.FACTORY.rows(new double[][] {{1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0},
{-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0},
{1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0},
{-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0}});

Primitive64Store tmpInequalityVector = Primitive64Store.FACTORY.rows({{0.1},{0.2},{0.2},{0.1},{0.2},{0.1},{0.1},{1.0},{1.0},{1.0},{1.0},{0.1},{1.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0}{0.0}{0.0},{0.0},{0.0},{1.0},{0.0}});

//calculating the Portfolio with the maximum return, this always seems to work fine
ConvexSolver tmpSolverMinDiversification = new ConvexSolver.Builder(tmpCOV.multiply(0), tmpR)
                .equalities(tmpEqualityMatrix, tmpEqualityVector).inequalities(tmpInequalityMatrix, tmpInequalityVector).build();
Optimisation.Result tmpResultMinDiversification = tmpSolverMinDiversification.solve();

//calculating the portfolio with minimal risk, this is where the error starts for me
ConvexSolver tmpSolverMaxDiversification = new ConvexSolver.Builder(tmpCOV, tmpR.multiply(0))
                .equalities(tmpEqualityMatrix, tmpEqualityVector).inequalities(tmpInequalityMatrix, tmpInequalityVector).build();
Optimisation.Result tmpResultMaxDiversification = tmpSolverMaxDiversification.solve();

我得到的结果如下：

具有最大回报的投资组合的权重

OPTIMAL -0.0455 @ { 0.1, 0.2, 0.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.4999999999999999 }

风险最小的投资组合权重

OPTIMAL 1.9065360317211953E-4 @ { -1.3215574127953212E-12, -3.0462153636587428E-12, 4.302357005267538E-12, 0.03119627351114846, 0.19999999989250858, 0.10000000045688691, -9.548402360338467E-13, 0.1370395162618518, 0.48451020053501254, 2.5326118583080594E-12, 0.03544670257704311, 0.011807307116290258, 6.086745301734428E-13 }

如果我添加一个额外的不等式（两者都有 1 个新行）约束并再次运行计算

Primitive64Store tmpInequalityMatrix = Primitive64Store.FACTORY.rows(new double[][] {{1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0},
{-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0},
{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0},
{1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0},
{-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0},
{-0.067,-0.045,-0.049,-0.01,-0.02,-1.0E-4,-0.034,-0.001,-0.006,-0.027,-0.005,-0.02,-0.04}});

Primitive64Store tmpInequalityVector = Primitive64Store.FACTORY.rows({{0.1},{0.2},{0.2},{0.1},{0.2},{0.1},{0.1},{1.0},{1.0},{1.0},{1.0},{0.1},{1.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0},{0.0}{0.0}{0.0},{0.0},{0.0},{1.0},{0.0},{ -0.037349326902676616 }});

ConvexSolver tmpSolverMaxDiversification = new ConvexSolver.Builder(tmpCOV, tmpR.multiply(0))
                .equalities(tmpEqualityMatrix, tmpEqualityVector).inequalities(tmpInequalityMatrix, tmpInequalityVector).build();
Optimisation.Result tmpResultEfficientPortfolio = tmpSolverMaxDiversification.solve();

我得到以下结果

OPTIMAL 0.004591387674786172 @ { 0.10000000000095524, 0.0, 0.20000000000667748, -3.148187023285784E-12, 0.19999999988537426, -2.6699549475823382E-11, 0.09999999999830238, 3.2126828658623563E-12, 7.645985136245771E-12, 0.5204239501042672, -0.12042395010749231, 1.4422465593413845E-12, -3.1890111868219504E-12 }

有没有办法避免那些约束破坏权重？我应该改用 ExpressionBasedModel 吗？

score 0 · Accepted Answer

如果你设置debug(ConvexSolver.class)一个实例Optimisation.Options并将其传递给你的构建方法，ConvexSolver.Builder那么你可能会得到一些关于出了什么问题的信息。

    Optimisation.Options options = new Optimisation.Options();
    
    options.debug(ConvexSolver.class);
    
    convexSolverBuilder.build(options);

ojalgo - ojalgo BUG：在 ojAlgo 中使用 ConvexSolver 时约束打破权重

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