Lagrange dual, weak duality and strong duality

Consider an optimization problem in standard form: with the variable . Let be the domain for , i.e. the intersection of the domains of the ‘s and the ‘s. Let denote the optimal value of the problem. The Lagrange dual function is the function defined as the minimum value of the Lagrangian over : The […]

Lagrange dual, weak duality and strong duality

Kolmogorov’s strong law of large numbers

The strong law of large numbers (SLLN) is usually stated in the following way: Theorem: For such that the ‘s are independent and identically distributed (i.i.d.) with finite mean , as , What if the ‘s are independent but not identically distributed? Can we say anything in that setting? We can if we add a […]

Kolmogorov’s strong law of large numbers