A function is convex if and only if its gradient is monotone. Stack Exchange Network 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
logic - Meaning of Monotone in Monotone Disjunction - Mathematics . . . The set of slides you link to speaks of "monotone disjunctions" in a particular AI context, and the terse woirding "no negations" makes sense only in this implicit context It is common in this area to consider disjunctive clauses of the form $$ x \lor y \lor \neg z \lor w \lor \cdots \lor \neg u $$ -- that is, a disjunction of input variables
Strong convexity and strong monotonicity of the sub-differential Stack Exchange Network 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
Monotone convergence theorem for series (basic proof) My question is how to prove monotone convergence theorem for infinite series without more advanced technique like counting measure I see this used a lot But looking through books like Rudin, the theorem for series or elementary proof is not to be found The theorem is: