Mathematical Method in Pheolegy

Mathematical Method and Proof

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria ...

A Mathematical Method for Managing the System Constraint

The goal of theory of constraints (TOC) is to maximize output, which is achieved byidentifying and managing the critically constrained resources. To manage the constraints, Goldrattproposed five focusing steps (5FS). If we increase constrained output, the output of system will beincreased. In this paper, we focus on step four of the 5FS and use the remained capacity of nonconstraintto elevate t...

A Sequential Method for Mathematical Programming

A sequential programming method for constrained optimization, which is referred to as SP method, is presented. It is based on a sequence of linearized constrained problems. Convergence and convergence rate of the method are analyzed based on solutions of the first order optimality conditions and on Lagrange multiplier theory. Unlike the SQP method, the SP method does not rely on an approximatio...

Isaac Newton on Mathematical Certainty and Method

A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method

A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar t...