Secondary condition

In various individual sciences, secondary conditions ( Latin restriction , also used in Germanized in Operations Research ) are those conditions that differ from the actual main condition, must also be met and thereby restrict the main condition.

Mathematics and natural sciences

In mathematics , the secondary condition is a condition for the variables that reduce the original definition of a function to a smaller amount. With functions of several variables, there are often constraints that limit the extreme value search. Constraints occur in optimization problems where an objective function should be minimized or maximized. The real difficulty is then presented by further requirements in the form of secondary conditions. In the case of the traveling salesman problem , for example , where the shortest route between several cities is to be found, certain cities must be visited in a certain time window. Optimization problems with a differentiable objective function, in which the secondary conditions are also differentiable functions, can be solved using Lagrange multipliers .

In differential-algebraic equations , differential equations are coupled with equations as constraints in which physical properties are modeled.

In physics, constraints limit the number of states that a system can assume to the realizable states of the system that meet these conditions. If, for example, there is a partition in a container that separates the left part from the right part, this partition creates a secondary condition if the left part is filled with a gas and the right part remains empty. The partition limits the realizable states of the gas to the left part of the container as long as it is not removed.

A secondary condition can describe a specification that results, for example, from the physical context or an additional specification that only enables a clear solution to the problem. Especially with physical problems one calls

Economics

In economics , secondary conditions play a role in target systems. In 1966, the business economist Edmund Heinen dealt with the target systems in companies , by which he understood at least two corporate goals that are related to one another. If the target system of an economic entity (company, private household , state ) contains several equal goals, it is essential for the decision-making whether the goals are in relation to each other in the relationship of total or partial complementarity or competition . Main goals can be set in mathematical decision models as “limited goals” in the form of secondary conditions.

Not every secondary condition can be interpreted as a limited goal. Formally, secondary conditions have the effect that from the set of value combinations for the individual action parameters, i.e. from the possible solutions of the decision model, those that are inadmissible are separated out. If the desired achievement of goals is to be limited, these are secondary conditions; in the case of unlimited achievement of goals, a goal fulfills its function in the narrower sense. This can be represented in a target relationship matrix.

In order to avoid conflicting goals between at least two competing goals, these goals must be arranged in a mutual ranking (goal hierarchy), which consists of a main goal and subordinate secondary goals (secondary conditions). As a result, competing goals no longer have to be fulfilled equally, but the goal classified as the main goal must first be fulfilled. The constraints may limit the main objective. In business administration , the other goals are considered secondary conditions that should not be met with priority but must be observed. They limit the fulfillment of the main goal; the entrepreneur only plans the maximum profit that arises under consideration of the secondary conditions. According to Heinz Kussmaul , the aim of all business decisions is long-term profit maximization under secondary conditions.

Types are

Individual evidence

1. Domschke et al .: Exercises and case studies on Operations Research , Springer, 8th edition, 2015, list of symbols + pp. 16f, 20, 25.
Schwenkert, Stry: Operatins Research Kompakt , Springer, 2015, pp. 5, 11, 232 .
Zimmermann: Operations Research , Vieweg, 2nd edition, 2008, pp 56, 71, 89th
2. Frederick Reif, Statistical Physics , 1985, p. 79
3. Edmund Heinen, The company's target system , 1966, p. 134
4. Edmund Heinen, The company's target system , 1966, p. 111
5. Edmund Heinen, The company's target system , 1966, p. 54