Related papers: A strong second-order sequential optimality condit…
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…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate…
This paper presents a twice continuously differentiable penalty function for nonlinear semidefinite programming problems. In some optimization methods, such as penalty methods and augmented Lagrangian methods, their convergence property can…
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict complementarity. In this paper we establish a condition of…
In this paper, we accomplish a unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems.Specifically, the…
We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…
Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivanov, Second-order optimality conditions for problems with…
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…
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…
This paper focuses on optimality conditions for $C^{1,1}$ vector optimization problems with inequality constraints. By employing the limiting second-order subdifferential and the second-order tangent set, we introduce a new type of…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
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…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
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…
Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…
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…
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global…
Optimality conditions are central to analysis of optimization problems, characterizing necessary criteria for local minima. Formalizing the optimality conditions within the type-theory-based proof assistant Lean4 provides a precise, robust,…
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…