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This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints (SDCMPCC).To achieve this goal, we first provide an exact characterization on the second-order…

Optimization and Control · Mathematics 2019-11-26 Yulan Liu , Shaohua Pan

One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality…

This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…

Optimization and Control · Mathematics 2024-10-01 Cung The Anh , Nguyen Hai Ha Giang

This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…

Optimization and Control · Mathematics 2019-06-24 Constantin Christof , Gerd Wachsmuth

In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…

Optimization and Control · Mathematics 2017-12-29 Bui Trong Kien , Nguyen Van Tuyen , Jen-Chih Yao

The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…

Optimization and Control · Mathematics 2023-05-10 Moisés Rodrigues Cirilo do Monte , Valeriano Antunes de Oliveira

In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an…

Optimization and Control · Mathematics 2023-02-09 Patrick Mehlitz

In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…

Optimization and Control · Mathematics 2019-01-15 M. Soledad Aronna

Second-order optimality conditions for vector nonlinear programming problems with inequality constraints are studied in this paper. We introduce a new second-order constraint qualification, which includes Mangasarian-Fromovitz constraint…

Optimization and Control · Mathematics 2019-06-11 Vsevolod I. Ivanov

Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient…

Optimization and Control · Mathematics 2010-08-06 Hongwei Lou

This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…

Optimization and Control · Mathematics 2019-03-15 Nguyen Huy Chieu , Le Van Hien , Tran T. A. Nghia , Ha Anh Tuan

In this paper, we establish some second order necessary/sufficient optimality conditions for optimal control problems of stochastic evolution equations in infinite dimensions. The control acts on both the drift and diffusion terms and the…

Optimization and Control · Mathematics 2018-11-20 Qi Lu , Haisen Zhang , Xu Zhang

The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint sets. The main attention is paid to the two major…

Optimization and Control · Mathematics 2018-05-02 Do Sang Kim , Boris S. Mordukhovich , Tien-Son Pham , Nguyen Van Tuyen

Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…

Optimization and Control · Mathematics 2025-11-05 Xiang Liu , Mengwei Xu , Liwei Zhang

In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…

Optimization and Control · Mathematics 2020-11-06 Li Deng

In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator…

Optimization and Control · Mathematics 2023-01-27 Matúš Benko , Patrick Mehlitz

Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…

Optimization and Control · Mathematics 2025-02-25 William W. Hager

In this paper, we introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper extended real function. This derivative is harmonized with the classical higher-order Fr\'echet…

Optimization and Control · Mathematics 2018-05-24 Vsevolod I. Ivanov

In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for…

Optimization and Control · Mathematics 2024-01-31 Jasarat J. Gasimov , Nazim I. Mahmudov

In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint…

Optimization and Control · Mathematics 2019-05-14 Yi-Bin Xiao , Nguyen Van Tuyen , Ching-Feng Wen , Jen-Chih Yao