Related papers: Higher-order optimality conditions with an arbitra…
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…
In optimal control, extending the class of admissible controls is a common strategy to guarantee the existence of optimal solutions. However, such extensions may introduce a gap between the infimum of the original problem and the minimum of…
This paper is concerned with the sensitivity analysis of a class of parameterized fixed-point problems that arise in the context of obstacle-type quasi-variational inequalities. We prove that, if the operators in the considered fixed-point…
We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is…
If the $n-th$ order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Hence, its order can be reduced to the lower order. In this paper,…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
In this paper we study the radial epiderivative notion for nonconvex functions, which extends the (classical) directional derivative concept. The paper presents new definition and new properties for this notion and establishes relationships…
We propose an integral representation for the higher-order Fr\'echet derivative of analytic matrix functions $f(A)$ which unifies known results for the first-order Fr\'echet derivative of general analytic matrix functions and for…
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…
We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
In this paper convex optimization techniques are employed for convex optimization problems in infinite dimensional Hilbert spaces. A first order optimality condition is given. Let $f : \mathbb{R}^{n}\rightarrow \mathbb{R}$ and let $x\in…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations…
In this article, we obtain sharp conditions for the existence of the high order derivatives ($k$-th order) of intersection local time $ \widehat{\alpha}^{(k)}(0)$ of two independent d-dimensional fractional Brownian motions $B^{H_1}_t$ and…
This expository paper contains a concise introduction to some significant works concerning the Karush-Kuhn-Tucker condition, a necessary condition for a solution in local optimality in problems with equality and inequality constraints. The…
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization,…
The directional subdifferential of the value function gives an estimate on how much the optimal value changes under a perturbation in a certain direction. In this paper we derive upper estimates for the directional limiting and singular…