# Core Technology

Operational (tactical) and strategic mathematical models are used in the optimization decision process to determine more efficient and effective ways to control and manage a system or process. Mathematical models are routinely used in natural sciences (physics, biology), engineering (artificial intelligence, computer science) and social science (economics, political science). However, the lack of agreement between theoretical (mathematical) models and experimental measurement in any discipline often leads to important advances since better theories are developed. Optimization helps create better theories and improves systems/processes in many disciplines. The biggest challenge is to engage the designer, collect the appropriate data and determine the appropriate model (linear vs. nonlinear, deterministic vs. probabilistic, static vs. dynamic or discrete vs. continuous).

## Applied Algebra: Solving for Chocolate

Applying algebra in engineering and computer science has a number of advantages and can help solve a great host of problems, from helping Netflix give you better recommendations for what to watch tonight to keeping an airplane in the air. Expanding the use of algebra is a relatively new movement with promising implications. Read the […]

## Computer Architecture

Connect to this wiki page as a companion for the synthesis lecture Optimization and Mathematical Modeling in Computer Architecture, which explores using Mixed Integer Linear Programming (MILP) to solve challenging problems in the field. The book gives in depth case studies of four optimization problems in computer architecture. This companion page provides a brief overview and […]

## Economics and Game Theory

Making optimal use of scarce resources is the central theme of economics; constrained optimization lies at the heart of many economic applications. Roger Myerson (Game Theory: Analysis of Conflict, Harvard University Press, 1991) defines game theory as “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”. Optimization theory plays an important […]

## Mixed-Integer Quadratic Optimization: Algorithms and Complexity

Mixed-integer quadratic programming (MIQP) is the simplest yet arguably the most important class of mixed-integer nonlinear programming (MINLP) that contains two major sources of difficulties: discrete decision variables and nonlinearity in the objective function. Not only many important applications can be naturally modeled as MIQPs, but a variety of more general MINLPs can be reformulated […]

## PATH

The PATH solver for mixed complementarity problems (MCPs) was introduced in 1995 and has since become the standard against which new MCP solvers are compared. License The version that is downloadable from here (i.e. the file pathlib.zip in this directory) is free, but is limited to problems with no more than 300 variables and 2,000 […]

## Structural properties and strong relaxations for mixed integer polynomial optimization

Research in nonconvex nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) has witnessed a significant growth at the theoretical, algorithmic and software levels over the last few years. While these new classes of algorithms have already had a remarkable impact across science, engineering, and economics, there exist a variety of important applications that these methods […]

## Supply Chain

Supply Chain Management became a popular term in the mid-1990s but, even today, no clear definition of the term has emerged. Instead, for most academics and practitioners, supply chain management is a broad term that covers many functions, including but not limited to manufacturing, warehousing, and transportation, as well as supplier relationship management, inventory management, […]