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AGEC552 - introduction mathematical programming
Dr. Paul Preckel - Purdue University
80
Agriculture
Graduate
09/17/2013
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Term
what do slack variables represent?
 Definition
idle capacity: the difference between how much of resource is available and how much is used
Term
how many slack variables should exist in what type of LP problem?
 Definition
maximization problem - 1 one slack variable is added to each structural constraint in the problem (excluding non-negativity)
Term
In GAMS, what are objects?
 Definition
things you name [i.e. sets, parameters (including scalars and tables), variables, equations, models, etc.]
Term
DEFINE ACRONYM
 Definition
A GAMS data type used to give logical classification to data points.
Term
DEFINE ALIAS
 Definition
An alternative name for a set.
Term
DEFINE ASSIGNMENT
 Definition
The statement used to change values associated with an identifier.
Term
DEFINE BASIC
 Definition
A classification o f a row or column that is in the basis maintained by solution methods that use linear programming iterations.
Term
DEFINE BINDING
 Definition
An inequality constraint is binding when the value of the associated slack is zero.
Term
DEFINE BOUNDS
 Definition
Upper and lower limits on the possible values that a column may assume in a feasible solution. May be "infinite," meaning that no limit is imposed.
Term
DEFINE COLUMN
 Definition
aN INDIVIDUAL DECISION VARIABLE IN THE MODEL SEEN BY A SOLVER PROGRAM. mANY MAY BE ASSOCIATED WITH ON gams VARIABLE.
Term
DEFINE COMPILATION
 Definition
The initial phase of GAMS processing, when the program is being checked for syntax and consistency.
Term
DEFINE CONSTANT SET
 Definition
A set is constant if it remains unchanged. It has to be initialized with a set definition statement and cannot be changed using assignment statements. Sets used in domain definitions must be constant. Sets used in lag operations must be ordered as well. Sometimes the word static is used instead of constant.
Term
DEFINE CONSTRAIN
 Definition
A relationship between columns that must hold in a feasible solution. There may be many constraints associated with one GAMS equation.
Term
DEFINE CONTINUOUS
 Definition
There are two contexts. First, a classification of a function. A plot of the function values will be a line without breaks in it. Second, a classification of variables. A continuous variable may assume any value within its bounds.
Term
DEFINE CONTROLLING SETS (AKA. DRIVING SETS)
 Definition
The sets that determine the domain of definitions, or that control an index operation such as SUM.
Term
DEFINE (GAMS) COORDINATOR
 Definition
The person who looks after the administration of a GAMS system, and who will know what solvers are available and can tell you who to approach for help with GAMS problems. The person's name should be given in the online 'help' file. Unlikely to apply to personal computer versions.
Term
DEFINE DATA TYPES
 Definition
Each symbol or identifier has to be declared to be one of the six data types, which are SET, PARAMETER, VARIABLE, EQUATION, MODEL, AND ACRONYM. The keywords SCALAR and TABLE do not introduce separate data types but rather comprise a shorthand way to declare a symbol to be a PARAMETER that will use a particular format for specifying initial values.
Term
DEFINE DECLARATION
 Definition
The entry of a symbol and the specification of its data type. A declaration may include the specification of initial values, and then it is more properly called a definition.
Term
DEFINE DEFAULT
 Definition
The value used, or the action taken, if the user provides no information.
Term
DEFINE DEFINITION
 Definition
The definition of the algebraic relationships in an equation or the assignment of initial values to parameters or of elements to sets as part of the initial declaration of the identifier.
Term
DEFINITE DEFINITION STATEMENTS
 Definition
Units that describe symbols, assign initial values to them, and describe symbolic relationships. Some examples are the SET, PARAMETER, ABLE, VARIABLE, and MODEL statements, and the equation definition statement.
Term
DEFINE DIRECTION
 Definition
Either maximization or minimization, depending whether the user is interested is interested in the largest or the smallest possible value for the objective function.
Term
DEFINE DISCONINUOUS
 Definition
A classification of a function. A plot of the function values will be a line with breaks in it.
Term
DEFINE DISCRETE
 Definition
A discrete variable (type binary or integer) may not assume any value between the bounds, but must assume integer values .
Term
DEFINE DOLLAR CONTROL OPTION (or DIRECTIVE)
 Definition
Directives or options used to control input or output detail associated with the GAMS compiler.
Term
DEFINE DOLLAR OPERATOR
 Definition
An operator used for exception handling in assignment statements and in equation definitions.
Term
DEFINE DOMAIN CHECKING
 Definition
The check that ensure that only legal label combination s are used on every assignment to, or reference of, an identifier.
Term
DEFINE DOMAIN OF DEFINITION
 Definition
The label combinations whose data will be updated in an assignment statement, or that will generate an individual constraint in an equation definition.
Term
DEFINE DOMAIN RESTRICTION CONDITION
 Definition
The alteration to the domain of definition caused when a dollar operator is used on the left (of the =" in an assignment or of the ".." in an equation definition)
Term
DEFINE DYNAMIC SET
 Definition
A set is dynamic if it has been changed with an assignment statement. Dynamic sets cannot be used with lag operations or in domain definitions.
Term
DEFINE ENDOGENOUS
 Definition
Data values that change when a solve statement is processed. In GAMS most often associated with VARIABLES.
Term
define equation
 Definition
The GAMS data type used to specify required relationships between activity levels of variables.
Term
DEFINE EXECUTION
 Definition
The second phase of GAMS processing, when GAMS is actually carrying out data transformations or generating a model.
Term
DEFINE EXECUTION STATEMENTS
 Definition
Instructions to carry out actions such as data transformations, model solutions, and report generation. Some examples are the assignment and the OPTION, DISPLAY, LOOP, and SOLVE statements.
Term
DEFINE EXOGENOUS
 Definition
Data values known before a SOLVE statement is processed, and not changed by the solve. In GAMS most often parameters.
Term
DEFINE (EXPLANATORY) TEXT
 Definition
A description associated with an identifier or label.
Term
DEFINE EXPONENT
 Definition
A scale factor used to conveniently represent very large or small numbers.
Term
DEFINE EXTENDED ARITHMETIC
 Definition
The usual computer arithmetic is extended to include plus and minus infinity (+INF and -INF) and a special value for an arbitrarily small number (i.e., one which is close to zero) known as epsilon (EPS). Also, not available (NA) can be used to indicate missing data, and undefined (UNDF) is the result of any illegal operation. GAMS sallows extended arithmetic for all operations and functions. The library problem [CRAZY] demonstrates extended arithmetic by showing the results for all operations and functions.
Term
DEFINE FEASIBLE
 Definition
Often used to describe a model that has at least one feasible solution.
Term
DEFINE FEASIBLE SOLUTION
 Definition
A solution to a model in which all column activity levels are within the bounds and all the constraints are satisfied.
Term
DEFINE HERCULES
 Definition
A system for formulating and solving macroeconomic models that are based on social accounting matrices.
Term
DEFINE IDENTIFIERS
 Definition
Names given to data entities. Also called symbols.
Term
DEFINE INDEX POSITION(S)
 Definition
Another way of describing the set(s) that must bed used when referencing a symbol of dimensionality one or more (i.e., a vector or a matrix).
Term
DEFINE INEQUALITY CONSTRAINT
 Definition
A constraint in which the imposed relationship between the columns is not fixed, but must be either greater than or equal to, or less than or equal to, a contrast. The GAMS symbols =G= AND =L= are used in equation definitions to specify these relationships.
Term
DEFINE INEQUALITY CONSTRAINT
 Definition
A constraint in which the imposed relationship between the columns is not fixed, but must be either greater than or equal to, or less than or equal to, a contrast. The GAMS symbols =G= AND =L= are used in equation definitions to specify these relationships.
Term
DEFINE INFEASIBLE
 Definition
Used to describe either a model that has no feasible solution, or an intermediate solution that is not feasible (although feasible solutions may exist).
Term
DEFINE INITIALIZATION
 Definition
Association initial values with sets or parameters using lists as part of the declaration or definition, or (for parameters only ) using TABLE statements.
Term
DEFINE LABELS
 Definition
Set elements. Sometimes called unique elements.
Term
DEFINE LIST
 Definition
One of the ways of specifying initial values. used with sets or parameters, most often for one dimensional but also for two and higher dimensional data structures.
Term
DEFINE LIST FORMAT
 Definition
One of the ways in which sets and parameters, can be initialized and all symbol classes having data can be displayed. Each unique label combination is specified in full, with the associated non-default value alongside.
Term
DEFINE MARGINALS
 Definition
Often called reduced costs or dual values. The values, which are mearningful only for nonbasic rows or columns in optimal solutiouns, contain information aboutthe rate at which the objective value will change of if the associated bound or right hand side is changed.
Term
DEFINE MATRIX ELEMENT (aka NONZERO ELEMENT)
 Definition
The coefficient of a particular column in a particular row if it is nonzero. Most mathematical programming problems are sparse, meaning that only a small proportion of the entries in the full tableau of dimensions "numbers of rows" by "number columns" is different from zero.
Term
DEFINE MODEL GENERATION
 Definition
The initial phase of processing a SOLVE statement: preparing a problem description for the solver.
Term
DEFINE MODEL LIST
 Definition
A list of equations used in a model, as specified in a MODEL statement.
Term
DEFINE NONBASIC
 Definition
A clumn that is not basic and (in nonlinear problems) not superbasic. Its value will be the same as one of the finite bounds (or zero if there are no finite bounds) if the solution is feasible.
Term
DEFINE NONLINEAR NONZERO
 Definition
In a linear programming problem, the nonzero elements are constant. In a nonlinear problem one or more of them vary because their values depend on that of one or more columns. The ratio of nonlinear (varying) to linear (constant) nonzero elements is a good indicator of the pervasiveness of nonlinearities in the problem
Term
DEFINE NONOPTIMAL
 Definition
There are two contexts. First, describing a variable: a nonbasic variable that would improve the objective value if made basic. The sign of the marginal value is normally used to test for nonoptimality. Second, for a solution: other solutions exist with better objective values.
Term
DEFINE NONSMOOTH
 Definition
A classification of a function that does not have continuous first derivatives, but has continuous function values. A plot of the function values will be a line with "kinks" in it.
Term
DEFINE NONZERO ELEMENT
 Definition
tHE COEFFICIENT OF A PARTICULAR COLUMN IN A PARTICULAR ROW IF IT IS NOT ZERO. mOST MATHEMATICAL PROGRAMMING PROBLEMS ARE SPARSE, MEANING THAT ONLY A SMALL PROPORTION OF THE ENTRIES IN THE FULL TABLEAU OF DIMENSIONS "NUMBER OF ROWS" BY "NUMBER OF COLUMNS IS DIFFERENT FROM ZERO."
Term
DEFINE OBJECTIVE ROW (or FUNCTION)
 Definition
Solver systems require the specification of a row or (for nonlinear systems) a function whose value will be maximized or minimized. GAMS users, in contrast, mus specify a scalar variable.
Term
DEFINE OBJECTIVE VALUE
 Definition
The current value of the objective row or of he objective variable.
Term
DEFINE OBJECTIVE VARIABLE
 Definition
The variable specified in he SOLVE statement.
Term
DEFINE OPTIMAL
 Definition
A feasible solution in which the objective value is the best possible.
Term
DEFINE OPTION
 Definition
The statement hat allows users to change the default actions or values in many different parts of the system.
Term
DEFINE ORDERED SETS
 Definition
A set is ordered if its content has been initiailzed wih a SET definition statement and the entry order of the indivudal elements of the set has the same patial order as the chronological order of the lebels. A set name alone on the left hand side of an assignemtn statement destroyes the ordered property. LAG and ORD operations rely on the relative position of the individual elements and therefore require ordered sets. Ordered sets are by definition constant.
Term
DEFINE OUTPUT
 Definition
The statement that allows users to change the default actions or values in many different pats o the system.
Term
DEFINE OUTPUT FILE
 Definition
A disk file containing output. A GAMS task produces one such file that can be inspected.
Term
DEFINE PARAMETER
 Definition
A constant or group of conStants that may be a scalar, a vector, or a matrix of two or more dimensions. One of the six data types in GAMS.
Term
DEFINE RELATIONAL OPERATOR
 Definition
This term may be used in two ways. First, in an equation definition it describes the type of relationship the equation specifies, for example equality, as specified with the =E= symbol. Second, in a logical expression, the symbols EQ, NE, LT, and so on are called relational operators, and are used to specify a required relationship between two values.
Term
DEFINE RIGHT HAND SIDE
 Definition
The value of the constant term in a constraint.
Term
DEFINE SCALAR
 Definition
One of the forms of PARAMETER inputs. Used for single elements.
Term
DEFINE SET
 Definition
A collection of elements (labels). The SET statement is used to declare and define a set.
Term
DEFINE SLACK
 Definition
The amount by which an inequality constraint is not binding
Term
DEFINE SLACK VARIABLE
 Definition
An artificial column introduced by a solver into a linear programming problem. Makes the implementation of the simplex method much easier.
Term
DEFINE SMOOTH
 Definition
A classification of a function that has continuous first derivatives.
Term
DEFINE SYMBOL
 Definition
An identifier.
Term
DEFINE TABLE
 Definition
One of the ways of initializing parameters. Used for two and higher dimensional data structures.
Term
DEFINE TEXT
 Definition
A description associated with an identifier or label.
Term
DEFINE VECTOR
 Definition
A one-dimensional array, corresponding to a symbol having one index position.
Term
DEFINE ZERO DEFAULT
 Definition
Parameter values are iniially zero. Other values can be initialized using PARAMETER or TABLE statements. Assignment statements have to be used thereafter o change parameter values.
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