What Is Optimization Toolbox?

2 TutorialTroubleshooting (Continued)ProblemWarning messages aredisplayed.The independentvariables, ,canonlytake on discrete values,for example, integers.RecommendationThis sometimes occurs when termination criteria are overly stringent,or when the problem is particularly sensitive to changes in theindependent variables. This usually indicates truncation or round-offerrors in the finite-difference gradient calculation, or problems inthe polynomial interpolation routines. These warnings can usuallybe ignored because the routines continue to make steps toward thesolution point; however, they are often an indication that convergencewill take longer than normal. Scaling can sometimes improve thesensitivity of a problem.This type of problem commonly occurs when, for example, thevariables are the coefficients of a filter that are realized usingfinite-precision arithmetic or when the independent variablesrepresent materials that are manufactured only in standard amounts.Although Optimization Toolbox functions are not explicitly set up tosolve discrete problems, you can solve some discrete problems by firstsolving an equivalent continuous problem. Do this by progressivelyeliminating discrete variables from the independent variables, whicharefreetovary.Eliminateadiscretevariablebyroundingitupordowntothenearestbest discrete value. After eliminating a discrete variable, solve areduced order problem for the remaining free variables. Havingfound the solution to the reduced order problem, eliminate anotherdiscrete variable and repeat the cycle until all the discrete variableshave been eliminated.dfildemo is a demonstration routine that shows how filters withfixed-precision coefficients can be designed using this technique.(From the MATLAB Help browser or the MathWorks Web sitedocumentation, you can click the demo name to display the demo.)2-100