Question: Solve the attached question: Consider the following optimization problem in (1:, y) E R X R: 1 minimize 5H3: :9!2 subject to a: E X,

Solve the attached question:

Consider the following optimization problem in (1:, y) E R" X R": 1 minimize 5H3: :9!\"2 subject to a: E X, :1; G Y, where X C R\" and Y C R" are nonempty, closed, convex, and disjoint sets (i.e.j XY=0). (a) Argue that the problem always has a solution (59*, y\"). (b) Write down the optimality condition for this problem, and determine the relations that .1" and 31* satisfy. Hint: the relations are in terms of the projections on the sets

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