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...
Trust-region method (TRM) is one of the most important numerical optimization methods in
solving nonlinear programming (NLP) problems. It works in a way that first define a region
around the current best solution, in which a certain model (usually a quadratic model) can to
some extent approximate the original objective...
An algorithm is a line search method if it seeks the minimum of a defined nonlinear function by selecting a
reasonable direction vector that, when computed iteratively with a reasonable step size, will provide a function
value closer to the absolute minimum of the function. Varying these will change the...
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...
Outer approximation is a basic approach for solving Mixed Integer Nonlinear Programming (MINLP) models
suggested by Duran and Grossmann (1986) . Based on principles of decomposition, outer-approximation and
relaxation, the proposed algorithm effectively exploits the structure of the original problems. The new problems
consist of solving an alternating finite sequence...
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...
The organization of general design problems into programming models allows for the defining and finding of their
(global) optimal solution. MINLP models represent problems as a sets of continuous variables with binary integer
variables. The continuous variables are restricted to defined constraints, and the binary variables represent whether
or not...
The Branch and Bound (BB or B&B) algorithm is first proposed by A. H. Land and A. G. Doig in 1960 for
discrete programming. It is a general algorithm for finding optimal solutions of various optimization problems,
especially in discrete and combinatorial optimization. A branch and bound algorithm consists 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...
The generalized disjunctive programming (GDP) was first introduced by Raman and Grossman (1994). The GDP extends
the use of (linear) disjunctive programming (Balas, 1985) into mixed-integer nonlinear programming (MINLP) problems,
and hence the name. The GDP enables programmers to solve the MINLP/MILP optimization problems by applying a
combination of algebraic...