In this paper, the problem of input signal design with the property that the estimated model satisfies a given performance level with a prescribed probability is studied. The aforementioned performance level is associated with a particular application. This problem is well-known to fall within the class of chance-constrained optimization problems, which are nonconvex in most cases. Convexificat...

Stability analysis of discrete-time switched systems under minimum dwell-time is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed by Geromel and Colaneri in [12]. The convexification of the conditions is performed by a lifting process which introduces a moderate number of additio...

Recursive McCormick relaxations are among the most popular convexification techniques for binary polynomial optimization. It is well-understood that both quality and size of these depend on recursive sequence finding an optimal amounts to solving a difficult combinatorial optimization problem. We prove any relaxation implied by extended flower relaxation, linear programming which problems with ...

We consider the problem of packing congruent circles with the maximum radius in a unit square. As a mathematical program, this problem is a notoriously difficult nonconvex quadratically constrained optimization problem which possesses a large number of local optima. We study several convexification techniques for the circle packing problem, including polyhedral and semi-definite relaxations and...

Convexification is a fundamental technique in (mixed-integer) nonlinear optimization and many convex relaxations are parametrized by variable bounds, i.e., the tighter the bounds, the stronger the relaxations. This paper studies how bound tightening can improve convex relaxations for power network optimization. It adapts traditional constraintprogramming concepts (e.g., minimal network and boun...

Simple polygons can be made convex by a finite number of flips, or of flipturns. These results are extended to very general polygons.