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The relational operators have the following meanings:
=l= less than or equal to
=g= greater than or equal to
=e= equal to
7 Objective Function 17
• It is important to understand the difference between the symbols '=' and '=e='. The '=' symbol is used only in direct
assignments, and the '=e=' symbol is used only in equation definitions. These two contexts are very different. A direct
assignment gives a desired value to a parameter before the solver is called. An equation definition also describes a
desired relationship, but it cannot be satisfied until after the solver is called. It follows that equation definitions must
contain variables and direct assignments must not.
• Variables can appear on the left or right-hand side of an equation or both. The same variable can appear in an equation
more than once. The GAMS processor will automatically convert the equation to its equivalent standard form (variables
on the left, no duplicate appearances) before calling the solver.
• An equation definition can appear anywhere in the GAMS input, provided the equation and all variables and parameters
to which it refers are previously declared. (Note that it is permissible for a parameter appearing in the equation to be
assigned or reassigned a value after the definition. This is useful when doing multiple model runs with one GAMS
input.) The equations need not be defined in the same order in which they are declared.

In Section The Dollar Condition, we describe how to use the dollar operator to impose restrictions on the summation operator
so that only the elements of i and j that satisfy specified conditions are included in the summation.
Products are defined in GAMS using exactly the same format as summations, replacing Sum by Prod. For example,
prod(j, x(i, j))
is equivalent to: Pjxi j.
Summation and product operators may be used in direct assignment statements for parameters. For example,

Sets
Sets are the basic building blocks of a GAMS model, corresponding exactly to the indices in the algebraic representations of
models. The Transportation example above contains one Set statement:

立的模型和用户界面
面向对象的GAMA API允许GAMS无缝整合到为交互提供适当类别的应用中。这三个面向对象GAMS API是.NET, Java
和Python与.NET framework 4 (Visual Studio 2010)、Java SE 5或更高版本以及Python 3.4, 2.7和2.6。
除了面向对象的GAMA API,还有级别(或级别) 的GAMS API,它们的使用要求有高深知识的GAMS组件库。
除了API, GAMS还提供智能链接到应用程序,如MS Excel, MatLab或R。用户可以在这个环境中继续工作,通过一个
API就可以访问GAMS所有的优化功能。这就允许应用中的模型数据和结果可以可视化和分析了。
**过120多个国家的不同领域的跨国公司、学校、研究机构和使用GAMS,包括能源化工、经济建模、农业规
划或制造业。
Independence of Model and User Interface
The GAMS object-oriented APIs allow the seamless integration of GAMS into an application by providing appropriate classes for the interaction with GAMS. The three versions of the object-oriented GAMS API: .NET, Java, and Python work with .NET framework 4 (Visual Studio 2010), Java SE 5 and up, as well as Python 3.4, 2.7, and 2.6 accordingly.
In addition to the object-oriented GAMS APIs, there are expert-level (or low-level) GAMS APIs whose usage requires advanced knowledge of GAMS component libraries. See our documentation for further information on the APIs.
In addition to the APIs, GAMS offers smart links to applications like MS Excel, MatLab, or R. Through these, the user can keep working in his productive tool environment, while the application accesses all optimization capabilites of GAMS through an API. This allows for example the visualization and analyses of model data and results in the application.
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