All Questions

Let $H$ be a separable Hilbert space (of non-zero dimension), let $(\Omega,\Sigma,\mu)$ be a finite measure space, and let $L^2(\mu;H)$ be the Bochner-space $\mu$-integrable $H$-valued functions. ...

Problem Statement I am looking for formal proof---hopefully textbook material---of two items: an analogue to Slater's condition [1] that obtains strong duality for optimization of convex functionals; ...

I am concerned with proving the existence of the dual of an infinite linear program. In addition to the writings of Rockafellar, Luenberger, and Boyd & Vandenberghe on: subdifferentials, Legendre-...

Let $X$ be an open set in $\mathbb{R}^n$ and $M(X)$ be the space of finite signed measures defined on $X$. $L(p)$ is a lower-semicontinuous convex functional defined on $M(X)$. My question is: (1) ...

Studying some problems arising in decision-making under model uncertainty, I'm led to consider the following problems. Let $\mathbb E_P$ and $\mathbb V_P$ denote the expectation and variance ...