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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

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

We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…

Optimization and Control · Mathematics 2026-03-30 Stefano Bosi , David Desmarchelier , Ngoc-Sang Pham

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…

Optimization and Control · Mathematics 2011-10-21 B. S. Mordukhovich , R. T. Rockafellar

We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…

Analysis of PDEs · Mathematics 2010-08-10 Mahouton Norbert Hounkonnou , Pascal Dkengne Sielenou

This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…

Optimization and Control · Mathematics 2026-05-20 Vu Huu Nhu , Nguyen Hai Son , Phan Quang Sang , Tran Duy

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

Optimization and Control · Mathematics 2021-11-01 Ashkan Mohammadi , Boris Mordukhovich

In this article, we prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in minimizing the time spent by solutions of a controlled…

Optimization and Control · Mathematics 2019-02-15 Laurent Pfeiffer , Terence Bayen

A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…

Optimization and Control · Mathematics 2025-01-22 Serge Gratton , Sadok Jerad , Philippe L. Toint

We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…

Optimization and Control · Mathematics 2013-01-30 M. Barbero-Liñán , B. Jakubczyk

This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…

Optimization and Control · Mathematics 2025-07-18 Xiaoxiao Ma , Wei Ouyang , Jane Ye , Binbin Zhang

In the last two decades, the sequential optimality conditions, which do not require constraint qualifications and allow improvement on the convergence assumptions of algorithms, had been considered in the literature. It includes the work by…

Optimization and Control · Mathematics 2025-01-27 Ellen H. Fukuda , Kosuke Okabe

This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by…

Optimization and Control · Mathematics 2019-11-06 Patrick Mehlitz , Alain B. Zemkoho

In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…

Optimization and Control · Mathematics 2025-02-14 Li Deng

In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the…

Optimization and Control · Mathematics 2022-03-10 Bruno F. Lourenço , Ellen H. Fukuda , Masao Fukushima

In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…

Computational Complexity · Computer Science 2017-02-15 Gabriel Haeser , Hongcheng Liu , Yinyu Ye

This paper investigates constrained nonsmooth multiobjective fractional programming problem (NMFP) in real Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional…

Optimization and Control · Mathematics 2024-03-18 Jiawei Chen , Luyu Liu , Yibing Lv , Debdas Ghosh , 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

This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…

Optimization and Control · Mathematics 2022-06-01 Teemu Pennanen , Ari-Pekka Perkkiö

We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…

Optimization and Control · Mathematics 2025-12-09 Guangdong Jing