We analyze in this work a spatio-temporal optimal design problem governed by a linear damped 1-D wave equation. The problem consists in seeking simultaneously the spatiotemporal layout of two isotropic materials and the static position of the damping set in order to minimize a functional depending quadratically on the gradient of the state. The lack of classical solutions for this kind of nonli...

Sequential quadratic programming (SQP) methods are a popular class of methods for nonlinearly constrained optimization. They are particularly effective for solving a sequence of related problems, such as those arising in mixed-integer nonlinear programming and the optimization of functions subject to differential equation constraints. Recently, there has been considerable interest in the formul...

This paper addresses the problem regarding optimal placement and sizing of distribution static synchronous compensators (D-STATCOMs) in electrical networks via a stochastic mixed-integer convex (SMIC) model complex domain. The proposed employs convexification technique based on relaxation hyperbolic constraints, transforming nonlinear programming into one. nature renewable energy demand is take...

This paper introduces in a natural way notion of horizontal convex envelopes continuous functions the Heisenberg group. We provide convexification process to find envelope constructive manner. also apply show h-convexity viscosity solutions class fully nonlinear elliptic equations group satisfying certain symmetry condition. Our examples that general one cannot expect without