Elements of Structural Optimization pp 71-114 | Cite as

# Linear Programming

## Abstract

Mathematical programming is concerned with the extremization of a function *f* defined over an *n*-dimensional design space **R** ^{ n } and bounded by a set **S** in the design space. The set **S** may be defined by equality or inequality constraints, and these constraints may assume linear or nonlinear forms. The function *f* together with the set **S** in the domain of *f* is called a *mathematical program* or a mathematical programming problem. This terminology is in common usage in the context of problems which arise in planning and scheduling which are generally studied under operations research, the branch of mathematics concerned with decision making processes. Mathematical programming problems may be classified into several different categories depending on the nature and form of the design variables, constraint functions, and the objective function. However, only two of these categories are of interest to us, namely *linear* and *nonlinear programming* problems (commonly designated as LP and NLP, respectively).

## Keywords

Objective Function Design Variable Linear Programming Problem Collapse Load Basic Feasible Solution## Preview

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