Concrete Structure Design Using Mixed-Integer

concrete structure design using mixed-integer

In this paper, we present a new class of problems of the following form: min f ðx; yÞ subject to gi ðx; yÞ ≥ 0 ∀i ∈ I 1 ; hi ðx; yÞ ¼ 0 ∀i ∈ I 2 ; 0 ≤ F i ðxÞ ⊥ xi ≥ 0 ∀i ∈ I 3 ; y∈Y integer; where I 1 , I 2 , and I 3 are (distinct) sets containing indices of functions associated with inequality, equality, and complementarity constraints, respectively; f ð·Þ, gð·Þ, and hð·Þ are twice continuously differentiable nonlinear functions; and the complementarity constraints in I 3 indicate that F i ðxÞ and xi are nonnegative, and at most one of the two is