Related papers: Higher-order optimality conditions with an arbitra…
In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…
In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are…
We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles naturally come from primal-dual framework, barrier smoothing, inexact computations of…
The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
In a recent paper [9], Ozdemir, Tunc and Akdemir defined two new classes of convex functions with which they proved some Hermite-Hadamard type inequalities. As an Open problem, they asked for conditions under which the composition of two…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
We study the gradient and higher order derivative estimates for the transmission problem in the presence of closely located inclusions. We show that in two dimensions, when relative conductivities of circular inclusions have different…
The Schwarzian derivative of a function f(x) which is defined in the interval (a, b) having higher order derivatives is given by Sf(x)=(f''(x)/f'(x))'-1/2(f''(x)/f'(x))^2 . A sufficient condition for a function to behave chaotically is that…
The unconstrained minimization of a sufficiently smooth objective function $f(x)$ is considered, for which derivatives up to order $p$, $p\geq 2$, are assumed to be available. An adaptive regularization algorithm is proposed that uses…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…
Two are the main objectives of this article: first, we introduce a method for determining and analyzing constrained local extrema that provides a different alternative to all previous works on the topic, by eliminating Lagrange multipliers…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
We propose and analyze a class of second-order dynamical systems for continuous-time optimization that incorporate fractional-order gradient terms. The system is given by \begin{equation} \ddot{x}(t) + \frac{\alpha}{t}\dot{x}(t) +…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
We introduce an extended tangent cone of high order to a set and study its properties. Then we use this local approximation for deriving high-order necessary conditions for local minimizers of constrained optimization problems.
This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of a novel Lyapunov function along with the…