blocks|key|2721226|text|您发布的代码有两个问题：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2721227|2721228|发布的Dmat实际上不是对称的；您意外地包含了值212.31581而不是12.31581|unordered-list-item|offset|length|style|CODE|2721229|+meq=2选项意味着您的前两个约束保持相等，这意味着您的权重总和为1，而您的回报恰好为5.2%25。第二个约束显然是导致不可行性的原因；考虑到您的其他约束，似乎没有有效的投资组合的回报率完全等于5.2%25。事实上，由于不超过一半的投资组合可以有3.33%25的回报，其余的必须至少有9.07%25的回报，所以回报必须是6.2%25或更高。因此，您应该通过设置meq=1.|2721230|将其放宽为>=约束|2721231|下面是工作代码：|2721232|library(quadprog)
Dmat+<-+matrix(c(356.25808,+12.31581,+261.88302,+12.31581,+27.24840,+18.50515,+261.88302,+18.50515,535.45960),+nrow=3,+ncol=3)
dvec+<-+matrix(c(9.33,+3.33,+9.07),+nrow=3,+ncol=1)
A.Equality+<-+matrix(c(1,1,1),+ncol=1)
Amat+<-+cbind(A.Equality,+dvec,+diag(3),+-diag(3))
bvec+<-+c(1,+5.2,+rep(0,+3),+rep(-0.5,+3))
qp+<-+solve.QP(Dmat,+dvec,+Amat,+bvec,+meq=1)
qp$solution
#+[1]+0.3808733+0.5000000+0.1191267|code-block|syntax|javascript|2721233|最优解决方案实际上与6.3%25的回报率相关。|2721234|entityMap^0|0|0|3|4|0|1|5|4R|5|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|Y|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|Z|8|@]|9|@]|A|$]]|$1|C|3|D|5|E|7|10|8|@$F|11|G|12|H|I]]|9|@]|A|$]]|$1|J|3|K|5|E|7|13|8|@$F|14|G|15|H|I]|$F|16|G|17|H|I]]|9|@]|A|$]]|$1|L|3|M|5|6|7|18|8|@]|9|@]|A|$]]|$1|N|3|O|5|6|7|19|8|@]|9|@]|A|$]]|$1|P|3|Q|5|R|7|1A|8|@]|9|@]|A|$S|T]]|$1|U|3|V|5|6|7|1B|8|@]|9|@]|A|$]]|$1|W|3|-4|5|6|7|1C|8|@]|9|@]|A|$]]]|X|$]]

There were two issues with the code you posted:

<ul>
<li>The posted <code>Dmat</code> is not actually symmetric; you had accidentally included value 212.31581 instead of 12.31581</li>
<li>The <code>meq=2</code> option means your first two constraints are held at equality, meaning your weights sum to 1 and your return is exactly 5.2%. The second constraint is apparently the one causing the infeasibility; it seems there are no valid portfolios that have return exactly equal to 5.2% given your other constraints. Indeed, since no more than half the portfolio can have return 3.33% and the rest must have return of at least 9.07%, the return must be 6.2% or greater. Therefore, you should relax this to a >= constraint by setting <code>meq=1</code>.</li>
</ul>

Here's the working code:

<pre><code>library(quadprog)
Dmat &lt;- matrix(c(356.25808, 12.31581, 261.88302, 12.31581, 27.24840, 18.50515, 261.88302, 18.50515,535.45960), nrow=3, ncol=3)
dvec &lt;- matrix(c(9.33, 3.33, 9.07), nrow=3, ncol=1)
A.Equality &lt;- matrix(c(1,1,1), ncol=1)
Amat &lt;- cbind(A.Equality, dvec, diag(3), -diag(3))
bvec &lt;- c(1, 5.2, rep(0, 3), rep(-0.5, 3))
qp &lt;- solve.QP(Dmat, dvec, Amat, bvec, meq=1)
qp$solution
# [1] 0.3808733 0.5000000 0.1191267
</code></pre>

The optimal solution is actually associated with a 6.3% return.

I am trying to use solve.QP to solve a portfolio optimization problem (quadratic problem)

Total 3 assets

There are 4 constraints:

<ol>
<li>sum of weights equal to 1</li>
<li>portfolio expected return equals to 5.2%</li>
<li>each asset weight greater than 0</li>
<li>each asset weight smaller than .5</li>
</ol>

Dmat is the covariance matrix

<pre><code>Dmat &lt;- matrix(c(356.25808, 12.31581, 261.8830, 212.31581, 27.24840, 18.50515, 261.88302, 18.50515,535.45960), nrow=3, ncol=3)
</code></pre>

dvec is each asset's expected return

<pre><code>dvec &lt;- matrix(c(9.33, 3.33, 9.07), nrow=3, ncol=1)
</code></pre>

Amat is the constraint matrix

<pre><code>A.Equality &lt;- matrix(c(1,1,1), ncol=1)
Amat &lt;- cbind(A.Equality, dvec, diag(3), -diag(3))
</code></pre>

constraint A^T b >= b_0, b vector

<pre><code>bvec &lt;- c(1, 5.2, rep(0, 3), rep(-0.5, 3))
</code></pre>

meq=2, since there are two equality constraints, first and second constraints are equality

Then I run the function solve.QP

<pre><code>library(quadprog)
qp &lt;- solve.QP(Dmat, dvec, Amat, bvec, meq=2)
</code></pre>

But it gives the error

<pre><code>Error in solve.QP(Dmat, dvec, Amat, bvec, meq = 2) : constraints are inconsistent, no solution!
</code></pre>

I am not sure where I did wrong.

r - Portfolio Optimization - solve.QP - Constraints are Inconsistent

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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我正在尝试使用solve.QP来解决投资组合优化问题(二次问题)。总计3项资产有4个约束：权重之和等于1投资组合预期收益等于5.2%每个资产权重大于0每个资产权重小于.5Dmat是协方差矩阵Dmat <- matrix(c(356.25808, 12.31581, 261.8830, 212.31581, 27.248...

R-投资组合优化- solve.QP -约束不一致-腾讯云开发者社区-腾讯云

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