Related papers: Necessary Optimality Conditions for Continuous-Tim…
The purpose of this paper is to prove the existence of solutions of quasi-equilibrium problems without any generalized monotonicity assumption. Additionally, we give an application to quasi-optimization problems.
In this workshop, we present a compact but rigorous introduction to the basic language of nonlinear programming, variational inequalities, and complementarity systems. The goal is twofold. First, we explain the mathematical logic of…
In many applications, including Stackelberg games, machine learning, and power systems \cite{Mackay2018Selftuning,Heinrich1952The,Wang2021Bi-Level}, the decisions in a minimax optimization problem can be constrained by a solution to an…
In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality…
We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the…
We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we…
As is well known, average-cost optimality inequalities imply the existence of stationary optimal policies for Markov Decision Processes with average costs per unit time, and these inequalities hold under broad natural conditions. This paper…
In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk…
In this paper, we obtain a new proof of Fritz John necessary optimality conditions for vector problems applying Kakutani fixed point theorem and Hadamard directional derivative. We also derive a similar proof of second-order Fritz John…
We prove an extension of Yuan's Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A. Trad. On the classical necessary second-order optimality…
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…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.
We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al. (2014)) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust…
We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Main results are higher-order Euler-Lagrange and DuBois-Reymond necessary optimality conditions as well as a higher-order…
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…
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…
In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…