Tracking nonlinear equilibrium paths by a homotopy method

Solving nonlinear programming problems via a homotopy continuation method under three unbounded conditions

“…As for how to trace the homotopy path numerically, there have been many predictor-corrector algorithms; see [1,3,4], etc., for references. Hence we omit this in this paper.…”

Application of normal flow algorithm in modal adaptive Pushover analysis

“…Step 2: The minimum solution of the norm is calculated, using the following equation, (20) in which {δ I } j i is the vector of tangential displacement in the point of convergence in step i − 1.…”

“…with this aim, sequential iterations of the Newton-Raphson method have been conducted along the path normal to the Davidenko flow curves, [19,20]. The non-linear system of equations governing the problem and the structure equilibrium path, F ∈ R N , is as follows,…”

“…It must be noted that Eq. (14) has an infinite number of solutions, but the minimum solution is unique, [20]. This solution can be found through two steps:…”

Nonlinear control using homotopy methods

“…Homotopy and continuation methods [2], [22] [23] are widely used techniques in numerical analysis. Especially for solving nonlinear algebraic equations they are a very powerful tool [ 111.…”