Given a set P of n points in the plane, we seek two squares whose center points belong to P , their union contains P , and the area of the larger square is minimal. We present eecient algorithms for three variants of this problem: In the rst the squares are axis parallel, in the second they are free to rotate but must remain parallel to each other, and in the third they are free to rotate indep...

We consider equilibrium constrained optimization problems, which have a general formulation that encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated KKM lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topol...

One approach to guaranteeing safety in Reinforcement Learning is through cost constraints that are dependent on the policy. Recent works constrained RL have developed methods ensure enforced even at learning time while maximizing overall value of Unfortunately, as demonstrated our experimental results, such approaches do not perform well complex multi-level tasks, with longer episode lengths or...

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using classical optimization methods, this paper presents a Multi-Objective Bees Algorithm (MOBA) for solving the multi-objective optimal of mechanical engineering problems design. In the pre...