# Shared Flashcard Set

## Details

AGEC552 - introduction mathematical programming
Dr. Paul Preckel - Purdue University
80
Agriculture
09/17/2013

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.
Supporting users have an ad free experience!