Documentation/Notation - Versionsgeschichte

Admin am 7. April 2019 um 12:31 Uhr

2019-04-07T12:31:38Z

2015-10-25T17:39:39Z

‎Terminology

2015-10-25T17:38:30Z

‎Terminology

2015-10-21T19:14:29Z

‎Symbols

2015-10-21T19:14:10Z

‎Symbols

2015-10-21T19:13:56Z

‎Symbols

2015-10-21T19:12:53Z

‎Terminology

2015-10-21T19:12:16Z

‎Terminology

2015-10-21T19:09:20Z

‎Terminology

2015-10-21T18:55:36Z

‎Terminology

@@ Zeile 1: / Zeile 1: @@
 == Notation ==
-As a math parser is currently not used, we write the math equations as formated text:
+As a maths parser is currently not used in this Wiki, we write math equations as formatted text:
 * Scalars are written as small italic letters, e.g. ''f''
 * Vectors are written as small bold letters, e.g. '''x'''.

@@ Zeile 28: / Zeile 28: @@
 :{| cellpadding="5" cellspacing="0" width="95%" border="1"
 |-
-| ''additionals''
+| ''additionals'' <div id="additionals"></div>
 | Additionals '''a''' are additional values in a '''solution''' that are for information only and do not influence the optimization. For example, if an optimization problem returns an objective function that is a sum of several values, these values could be added to the solution as additional values '''a'''.
 |-
-| ''constraints''
+| ''constraints'' <div id="constraints"></div>
 | Constraints '''g''' are criteria that have to be fulfilled. OpenDino defines a constraint ''g'' as
 * fulfilled, if  ''g'' =< 0
@@ Zeile 40: / Zeile 40: @@
 ''f'' + max(0, ''g'').
 |-
-| ''design variables''
+| ''design variables'' <div id="design_variables"></div>
 | The vector of design variables '''x''' may consist of real numbers (continuous variables), integers (discrete variables) or both (mixed variables).
 |-
-| ''objectives''
+| ''objectives'' <div id="objectives"></div>
 | An optimization problem must have at least one objective or one constraint. OpenDino requires that the objective(s) '''f''' is/are to be minimized. A maximization of a function ''k'' can be converted into minimization by using ''f'' = -''k''.
 |-

@@ Zeile 46: / Zeile 46: @@
 | An optimization problem must have at least one objective or one constraint. OpenDino requires that the objective(s) '''f''' is/are to be minimized. A maximization of a function ''k'' can be converted into minimization by using ''f'' = -''k''.
 |-
-| ''solution''
+| ''solution'' <div id="solution"></div>
 | The term solution is used in optimization. One solution ('''x''','''f''','''g''','''a''') consists of a vector of design variables '''x''', the evaluated objective(s) '''f'''('''x'''), constraint(s) '''g'''('''x'''), and optionally of additional values '''a'''.
 |-|}

@@ Zeile 15: / Zeile 15: @@
 | ''f'', '''f'''
 | objective function(s)
 |-
 | ''x'', '''x'''
 | design variable(s)
 |-
 |}

@@ Zeile 12: / Zeile 12: @@
 | ''a'', '''a'''
 | additionals, i.e. additional value(s)
 | ''f'', '''f'''
 | objective function(s)

@@ Zeile 29: / Zeile 29: @@
 |-
 | ''constraints''
-| Constraints '''c''' are criteria that have to be fulfilled. OpenDino defines a constraint ''c'' as
+| Constraints '''g''' are criteria that have to be fulfilled. OpenDino defines a constraint ''g'' as
-* fulfilled, if  ''c'' =< 0
+* fulfilled, if  ''g'' =< 0
-* violated, if  ''c'' > 0.
+* violated, if  ''g'' > 0.
 The most simple constraint handling in optimization is to add a penalty to the objective function if the constraint is vialoted, resulting in
-''f'' + max(0, ''c'').
+''f'' + max(0, ''g'').
 |-
 | ''design variables''

@@ Zeile 23: / Zeile 23: @@
 == Terminology ==
-:{| cellpadding="5" width="95%"
+:{| cellpadding="10" width="90%"
 |-
 | ''solution''
-| The term solution is used in optimization. One solution ('''x''','''f''','''g''') consists of a vector of design variables '''x''', the evaluated objective(s) '''f'''('''x''') and constraint(s) '''g'''('''x''')'''.
+| The term solution is used in optimization. One solution ('''x''','''f''','''g''','''a''') consists of a vector of design variables '''x''', the evaluated objective(s) '''f'''('''x'''), constraint(s) '''g'''('''x''')''', and optionally of additional values '''a'''.
 |-
 |}