Related papers: Second-order subdifferential. Extremal problems fo…
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…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
In this paper, we introduce the second-order subdifferentials for functions which are G\^ateaux differentiable on an open set and whose G\^ateaux derivative mapping is locally Lipschitz. Based on properties of this kind of second-order…
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…
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…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
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…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
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…
It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…
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…
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…
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…
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…
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…
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…
Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories…
This paper on the whole concerns with the duality of Mayer problem for k-th order differential inclusions, where k is an arbitrary natural number. Thus, this work for constructing the dual problems to differential inclusions of any order…