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For each slot , define: = = ()This function is a scalar measure of the total queue backlog in the network. It is called quadratic Lyapunov function on the queue state. . Define the Lyapunov drift as the change in this function from one slot to the
This usage is the same as that in the phrases linear programming and mathematical programming, a synonym for mathematical optimization. [ 18 ] The above explanation of the origin of the term may be inaccurate: According to Russell and Norvig, the above story "cannot be strictly true, because his first paper using the term (Bellman, 1952 ...
If the state space and action space are finite, we could use linear programming to find the optimal policy, which was one of the earliest approaches applied. Here we only consider the ergodic model, which means our continuous-time MDP becomes an ergodic continuous-time Markov chain under a stationary policy .
Linear vs. nonlinear. If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. A model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
Operations research (British English: operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making.
Linear methods can also be applied, but the engineer must manually specify the interactions when using them. When considering a new application, the engineer can compare multiple learning algorithms and experimentally determine which one works best on the problem at hand (see cross-validation ).
Since linear motion is a motion in a single dimension, the distance traveled by an object in particular direction is the same as displacement. [4] The SI unit of displacement is the metre . [ 5 ] [ 6 ] If x 1 {\displaystyle x_{1}} is the initial position of an object and x 2 {\displaystyle x_{2}} is the final position, then mathematically the ...