# An Adaptive Linear Programming Algorithm with Parameter Learning
## 6 Glossary  
Accumulated constraint(s): When a nonlinear constraint is concave (the degree of the convexity is lower than \(-0.015\)), the approximated linear constraint of the previous iteration is carried forward and combined with its approximated linear constraint in the current iteration. Thus, a concave nonlinear constraint is represented by multiple linear constraints, and those carried forward are called accumulated constraints.  
Active constraint: If the slack or surplus of a constraint at a solution point is zero, then it is an active constraint.  
Convexity degree: The average value of the diagonal terms of the Hessian matrix of a function. This definition is applied to any paper on the cDSP and ALP.  
Deviation: The percentage difference between the value of a goal at a solution and its target.  
DSIDES: DSIDES is short for decision support in the design of engineering systems, which is a computational platform for designers to formulate engineering design problems using the compromise decision support problem (cDSP) and linearize and solve the problems using the adaptive linear programming (ALP) algorithm.  
Parameter learning: This includes a set of activities to maximize the approximation performance--identifying the evaluation indices (EIs), the desired range of each evaluation index (DEI), and the value of a parameter, namely, the reduced move coefficient (RMC), that makes each EI fall into its desired range, DEI.  
Parameter tuning: This means finding the value of a parameter, namely, the reduced move coefficient (RMC), that makes each EI fall into its desired range, DEI. It is a part of parameter learning.  
[PERSON] was responsible for developing and implementing the advanced adaptive linear programming algorithm with parameter learning and writing this paper with input from her co-authors. [PERSON] is the originator of the adaptive linear programming (ALP) algorithm. [PERSON] is responsible for coding the algorithm; see [6]. [PERSON] incorporated the ALP algorithm into the decision support environment, DSIDES. He was instrumental in advising [PERSON] about the use of DSIDES and ensuring what is written is accurate; see [30]. [PERSON] provided the test example for [PERSON] to use in her dissertation. He was instrumental in advising [PERSON] about how the data were structured, the interpretation of the results, and ensuring that what is written is accurate; see [36]. [PERSON] and [PERSON] mentored [PERSON] complete her PhD dissertation. Both supported [PERSON] financially during her PhD program. Both revised and edited the manuscript. All authors have read and agreed to the published version of the manuscript.  
[PERSON] was supported by the LA Comp Chair and the John and Mary Moore Chair at the University of Oklahoma till August 2021, then is supported by the Pietz Professorship funds and the start-up fund from the Research Affairs Office at South Dakota School of Mines and Technology since September 2021. All the three funding sources are internal.  
**Data Availability Statement:** The data used in this work are taken from the publication by [PERSON] [36].  
**Acknowledgments:** We are grateful to the late [PERSON] for originating the adaptive linear programming (ALP) algorithm. We are grateful to [PERSON] for coding the ALP algorithm. We are grateful to [PERSON] and [PERSON] for their help in testing the ALPPL algorithm. [PERSON] acknowledges the Pietz Professorship funds and the start-up fund from the Research Affairs Office at South Dakota School of Mines and Technology. [PERSON] and [PERSON] gratefully acknowledge support from the LA Comp Chair and the [PERSON] Chair at the University of Oklahoma.  
**Conflicts of Interest:** On behalf of all authors, the corresponding author states that there is no conflict of interest.