I've been trying to solve the following optimization problem

$$

begin {array} {rl}

min limits _ { boldsymbol {w}} & boldsymbol {w} boldsymbol {C} boldsymbol {w} \

mbox {s.t.} & sum_ {j = 1} ^ K w_j = 1 \

end {array}

$$

Where $ boldsymbol {w} in mathbb {R} ^ K $ Y $ boldsymbol {C} in mathbb {R} ^ {K times K} $ Y $ boldsymbol {C} $ it is **symmetrical**, that is to say $ boldsymbol {C} = boldsymbol {C} ^ top $.

Enter lagrange multiplier $ lambda in mathbb {R} $ and build the Lagrangian using the vector $ boldsymbol {1} = (1, ldots, 1) ^ top in mathbb {R} ^ K $

$$

mathcal {L} ( boldsymbol {w}, lambda) = boldsymbol {w} boldsymbol {C} boldsymbol {w} – lambda ( boldsymbol {1} ^ top boldsymbol {w} – one )

$$

Then take the derivative with respect to $ boldsymbol {w} $

$$

nabla _ { boldsymbol {w}} mathcal {L} ( boldsymbol {w}, lambda) = 2 boldsymbol {C} boldsymbol {w} – lambda boldsymbol {1}

$$

However, I'm not sure how to solve this now …