Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
If I recall correctly, every proper, convex, lowerweak*-lower semi-continuous function is a conjugate. In fact, it is the conjugate of its pre-conjugate$$
f(x) = \sup_{x^*\in X^*} \langle x^*,x\rangle - g(x^*).
$$
If I recall correctly, every proper, convex, lower semi-continuous function is a conjugate. In fact, it is the conjugate of its pre-conjugate$$
f(x) = \sup_{x^*\in X^*} \langle x^*,x\rangle - g(x^*).
$$
If I recall correctly, every proper, convex, weak*-lower semi-continuous function is a conjugate. In fact, it is the conjugate of its pre-conjugate$$
f(x) = \sup_{x^*\in X^*} \langle x^*,x\rangle - g(x^*).
$$
If I recall correctly, every proper, convex, lower semi-continuous function is a conjugate. In fact, it is the conjugate of its pre-conjugate$$
f(x) = \sup_{x^*\in X^*} \langle x^*,x\rangle - g(x^*).
$$
