A quadratic function is concave if the coefficient of every squared term is negative and there is no cross term of decision variables.Group of answer choicesTrueFalse
Question
A quadratic function is concave if the coefficient of every squared term is negative and there is no cross term of decision variables.Group of answer choicesTrueFalse
Solution
The correct answer is "False."
Explanation:
A quadratic function is concave if the coefficient of every squared term is negative, but the absence of cross terms of decision variables is not a necessary condition for concavity.
In fact, a quadratic function can still be concave even if there are cross terms, as long as the matrix of coefficients of the quadratic terms (also known as the Hessian matrix) is negative semi-definite.
Therefore, the statement "A quadratic function is concave if the coefficient of every squared term is negative and there is no cross term of decision variables" is false.
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