Robust optimization is a subset of optimization theory that deals with a certain measure of robustness vs uncertainty. This balance of robustness
and uncertainty is represented as variability in the parameters of the problem at hand and or its solution [1]. In robust optimization, the modeler
aims to find decisions...
The chance-constrained method is one of the major approaches to solving optimization problems under various
uncertainties. It is a formulation of an optimization problem that ensures that the probability of meeting a certain
constraint is above a certain level. In other words, it restricts the feasible region so that the...
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...
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...
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...
Column generation algorithms are used for MILP problems. The formulation was initially proposed by Ford and
Fulkerson in 1958 . The main advantage of column generation is that not all possibilities need to be enumerated.
Instead, the problem is first formulated as a restricted master problem (RMP). This RMP has...
The traveling salesman problem (TSP) is a widely studied combinatorial optimization problem, which, given a set of cities and a cost to travel from one city to another, seeks to identify the tour that will allow a salesman to visit each city only once, starting and ending in the same...
Optimization with absolute values is a special case of linear programming in which a problem made nonlinear due
to the presence of absolute values is solved using linear programming methods.
Absolute value functions themselves are very difficult to perform standard optimization procedures on. They are
not continuously differentiable functions, are...