We consider feasible sets given by conic constraints, where the cone defining the constraints is convex with nonempty interior. We study the case where the feasible set is not assumed to be regular in the classical sense of Robinson and obtain a constructive description of the tangent cone under a certain new second-order regularity condition. This condition contains classical regularity as a s...

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the secondorder sufficient condition for optimality...

The aim of judgment aggregation is to make collective decisions based on the judgments of individual agents. Some rationality conditions governing the expected behavior of the aggregation function must be considered. However, impossibility theorems show that designing an aggregation function satisfying all desirable properties is not feasible. While some rationality conditions are very natural ...

There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques that are the cornerstones of static network flows. The aim of this paper is to advance the state of the art for dynamic network flows by developing the cont...

We develop and describe an iteratively corrected rational Krylov algorithm for the solution of the optimal H2 model reduction problem. The formulation is based on finding a reduced order model that satisfies interpolation based first-order necessary conditions for H2 optimality and results in a method that is numerically effective and suited for large-scale problems. We provide a new elementary...

This paper is concerned with the optimal distributed control problem governed by b-equation. We firstly investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary condition. By contrasting with our previous result, the proof without considering viscous coefficient is a big improvement. Secondly, based on the well-posedness res...

New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions – holding without any constraint qualification – are proved for singleor multi-objective constrained optimization prob...

In the first part of this two-paper series, we presented a conceptual algorithm for the optimal control of constrained switched systems and proved that this algorithm generates a sequence of points that converge to a necessary condition for optimality. However, since our algorithm requires the exact solution of a differential equation, the numerical implementation of this algorithm is impractic...

We study Siegel’s center problem on the linearization of germs of diffeomorphisms in one variable. In addition of the classical problems of formal and analytic linearization, we give sufficient conditions for the linearization to belong to some algebras of ultradifferentiable germs closed under composition and derivation, including Gevrey classes. In the analytic case we give a positive answer ...

An algorithm for solving continuous-time stochastic optimal control problems is presented. The numerical scheme is based on the stochastic maximum principle (SMP) as an alternative to the widely studied dynamic programming principle (DDP). By using the SMP, (Peng, 1990) obtained a system of coupled forwardbackward stochastic differential equations (FBSDE) with an external optimality condition. ...