Many aspects of social welfare are intrinsically multidimensional. Composite indices at-tempting to reduce this complexity to a unique measure abound in many areas of economics and public policy. Comparisons based on such measures depend, sometimes critically, on how the di erent dimensions of...

Many aspects of social welfare are intrinsically multidimensional. Composite indices at-tempting to reduce this complexity to a unique measure abound in many areas of economics and public policy. Comparisons based on such measures depend, sometimes critically, on how the different dimensions of...

We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere.These relatively simple optimization problems have many applications.We review known approximation results as well as negative (inapproximability) results from the...