What Is Optimization Toolbox?

fgoalattainPurposeEquationSolve multiobjective goal attainment problemsFinds the minimum of a problem specified byminimize γx,γsuch thatFx ( ) −weight⋅γ≤ goalcx ( ) ≤ 0ceq( x)= 0Aeq ⋅ x = beqlb ≤ x ≤ ubwhere x, weight, goal, b, beq, lb, andub are vectors, A and Aeq arematrices, and c(x), ceq(x), and F(x) are functions that return vectors.F(x), c(x), and ceq(x) can be nonlinear functions.SyntaxDescriptionx = fgoalattain(fun,x0,goal,weight)x = fgoalattain(fun,x0,goal,weight,A,b)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon)x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,... options)[x,fval] = fgoalattain(...)[x,fval,attainfactor] = fgoalattain(...)[x,fval,attainfactor,exitflag] = fgoalattain(...)[x,fval,attainfactor,exitflag,output] = fgoalattain(...)[x,fval,attainfactor,exitflag,output,lambda] = fgoalattain(...)fgoalattain solves the goal attainment problem, which is oneformulation for minimizing a multiobjective optimization problem.x = fgoalattain(fun,x0,goal,weight) triestomaketheobjectivefunctions supplied by fun attain the goals specified by goal by varyingx, startingatx0, with weight specified by weight.8-12