What Is Optimization Toolbox?

fgoalattainmethods assume the functions are continuous, the method is ableto make steps toward the solution because the discontinuities do notoccur at the solution point. When the objectives and goals are complex,fgoalattain tries to achieve the goals in a least-squares sense.AlgorithmMultiobjective optimization concerns the minimization of a set ofobjectives simultaneously. One formulation for this problem, andimplemented in fgoalattain, is the goal attainment problem ofGembicki [3]. This entails the construction of a set of goal values forthe objective functions. Multiobjective optimization is discussed fully inChapter 3, “Standard Algorithms”.In this implementation, the slack variable is used as a dummyargument to minimize the vector of objectives F(x) simultaneously;goal is a set of values that the objectives attain. Generally, prior tothe optimization, it is not known whether the objectives will reachthe goals (under attainment) or be minimized less than the goals(overattainment). A weighting vector, weight, controls the relativeunderattainment or overattainment of the objectives.fgoalattain uses a sequential quadratic programming (SQP)method, which is described fully in Chapter 3, “Standard Algorithms”.Modifications are made to the line search and Hessian. In the linesearch an exact merit function (see [1] and [4]) is used together withthe merit function proposed by [5]and [6]. The line search is terminatedwhen either merit function shows improvement. A modified Hessian,which takes advantage of the special structure of the problem, is alsoused (see [1] and [4]). A full description of the modifications used isfound in “Goal Attainment Method” on page 3-49 in “Introduction toAlgorithms.” Setting the MeritFunction option to 'singleobj' withoptions = optimset(options,'MeritFunction','singleobj')uses the merit function and Hessian used in fmincon.Seealso“SQPImplementation”onpage3-32formoredetailsonthe algorithm used and the types of procedures displayed under theProcedures heading when the Display option is set to 'iter'.8-26