Network Flow Optimization problems form the most special class of linear programming problems.
Transportation, electric, and communication networks are clearly common applications of Network Optimization.
These types of problems can be viewed as minimizing transportation problems. This Network problem will include
cost of moving materials through a network involving varying...
The objective of game theory is to analyze the relationship
between decision-making situations in order to achieve a
desirable outcome. The theory can be applied to a wide range
of applications, including, but not limited to, economics,
politics and even the biological sciences. In essence, game
theory serves as means...
Computational complexity refers to the amount of resources
required to solve a type of problem by systematic application of an
algorithm. Resources that can be considered include the amount of
communications, gates in a circuit, or the number of processors.
Because the size of the particular input to a problem...
Spatial branch-and-bound is a divide-and-conquer technique used to find the deterministic solution of global optimization
problems.1 It is a type of branch-and-bound method, which solves for the set of parameters that globally optimize the
objective function, whether that be finding the minimum or maximum value of or , respectively, where...
McCormick Envelopes are a type of convex relaxation used in
bilinear Non Linear Programming problems. Many times these
envelopes are used to solve a Mixed Integer Non Linear
Programming problem by relaxing the MINLP problem so that
it becomes a convex NLP. Solving this convex NLP will
provide a lower...
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...
This article concerns the exponential transformation method for globally solving posynomial (or general
geometric/signomial) optimization problems with nonconvex objective functions or constraints. A discussion of the
method's development and use will be presented.
Optimization and Game Theory have certain conceptual overlaps. It is even said that John von Neumann
conjectured the Duality Theorem using information from his game theory. This article discusses two optimization
applications to the game theory: a methodology for solving the Nash Equilibrium and a decentralized model in
supply chain...
Aerospace collectively represents one of the most sophisticated technological endeavors and largest markets in the
world. Coming with substantial costs, nearly every aspect of the industry, from aircraft design to material selection
to operation, has been optimized in at least one way. A critical design consideration in any aircraft is...