Sufficient and necessary global optimality conditions for nonlinear impulsive dynamic optimization problems with endpoint constraints are obtained. Proofs of these results are based on Hamilton-Jacobi canonical optimality theory. As consequence, a Maximum Principle reverse into sufficient optimality conditions is proposed.

We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and sufficient conditions for a critical point of the risk function to be a global...

We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state – by assuming weak hypotheses) constraints.