Geometric programming was introduced in 1967 by Duffin, Peterson and Zener. It is very useful in the applications
of a variety of optimization problems, and falls under the general class of signomial problems[1]. It can be used to
solve large scale, practical problems by quantifying them into a mathematical optimization...
The interior point (IP) method for nonlinear programming was pioneered by Anthony V. Fiacco and Garth P. McCormick in the
early 1960s. The basis of IP method restricts the constraints into the objective function (duality
( http://en.wikipedia.org/wiki/Duality_%28optimization%29) ) by creating a barrier function. This limits potential solutions to
iterate in only...
Extended Cutting Plane is an optimization method suggested by Westerlund and Petersson in 1996 to solve
Mixed-Integer NonLinear Programming (MINLP) problems . ECP can be thought as an extension of Kelley's
cutting plane method, which uses iterative Newton's method to refine feasible area and ultimately solve a problem
within tolerable...
J.F. Benders devised an approach for exploiting the structure of mathematical programming problems with complicating
variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more
tractable).The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for
building up adequate representations of...
General disjunctive programming, GDP, is an alternative approach to represent the formulation of traditional
Mixed-Integer Nonlinear Programming, solving discrete/continuous optimization problems. By using algebraic
constraints, disjunctions and logic propositions, Boolean and continuous variables are involved in the GDP
formulation. The formulation process of GDP problem are more intuitive, and the...
Interior point methods are a type of algorithm that are used in
solving both linear and nonlinear convex optimization
problems that contain inequalities as constraints. The LP
Interior-Point method relies on having a linear programming
model with the objective function and all constraints being
continuous and twice continuously differentiable. In...
Logarithmic transformation is a method used to change geometric programs into their convex forms. A
geometric program, or GP, is a type of global optimization problem that concerns minimizing a subject to
constraint functions so as to allow one to solve unique non-linear programming problems. All geometric programs
contain functions...