Related papers: Multipliers for nonlinearities with monotone bound…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
In the seminal book M\'echanique analitique, Lagrange, 1788, the notion of a Lagrange multiplier was first introduced in order to study a smooth minimization problem subject to equality constraints. The idea is that, under some regularity…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments…
In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.
Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. In this context, the present paper develops novel fixed-lag and…
In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem…
We show that an optimality condition of M-stationarity type holds for minimizers of a class of mathematical programs with complementarity constraints (MPCCs) in Lebesgue spaces. We apply these results also to local minimizers of an inverse…
We give some reasonable and usable conditions on a sequence of norm one in a dual banach space under which the sequence does not converges to the origin in the $w^*$-topology. These requirements help to ensure that the Lagrange multipliers…
This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to…
In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…
In various supersymmetric extensions of the Standard Model there appear non-topological solitons due to the existence of U(1) global symmetries associated with Baryon and/or Lepton quantum numbers. Trilinear couplings (A-terms) in the…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
This thesis is devoted to the study of multivariate (joint) spectral multipliers for systems of strongly commuting non-negative self-adjoint operators, $L=(L_1,\ldots,L_d),$ on $L^2(X,\nu),$ where $(X,\nu)$ is a measure space. By strong…
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…
This note studies the exponential convergence of input-output signals of discrete-time nonlinear systems composed of a feedback interconnection of a linear time-invariant system and a nonlinear uncertainty. Both the open-loop subsystems are…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…