Related papers: Second-order Optimality Conditions by Generalized …

This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the commonly used M-stationarity conditions and are in particular useful when the latter cannot…

The regularity of the Hardy-Littlewood maximal function, in both discrete and continuous contexts, and for both centered and noncentered variants, has been subjected to intense study for the last two decades. But efforts so far have…

It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…

This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…

We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…

Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…

In this paper, we obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute value are convex and concave.Finally, we gave some applications for special means.

We obtain regularity conditions of a new type of problems of the calculus of variations with second-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main result asserts that autonomous integral…

In this paper a second order dynamical system model is proposed for computing a zero of a maximal comonotone operator in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of a strong global solution of the proposed…

In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric…

We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of $A$ are discontinuous and $A$ is…

In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of…

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…

In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…

A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an…

In this work we introduce a formulation for a non-local Hessian that combines the ideas of higher-order and non-local regularization for image restoration, extending the idea of non-local gradients to higher-order derivatives. By carefully…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…