Related papers: Second Order Optimality Conditions and Improved Co…
We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in…
In this paper, we consider the cardinality-constrained optimization problems and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results…
The main goal of this paper is to relate the topologically relevant stationary points of a cardinality-constrained optimization problem and its continuous reformulation up to their type. For that, we focus on the nondegenerate M- and…
We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming…
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…
We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…
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…
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…
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 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…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the commonly used M-stationarity conditions and are in particular useful when the latter cannot…
In this paper we study second-order optimality conditions for non-convex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well-known that second-order optimality conditions involve the support…
In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective…
We consider the class of mathematical programs with orthogonality type constraints (MPOC). Orthogonality type constraints appear by reformulating the sparsity constraint via auxiliary binary variables and relaxing them afterwards. For MPOC…
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…
In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained…
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…
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…