Related papers: Second-Order Karush-Kuhn-Tucker Optimality Conditi…
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…
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 research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for…
Additive manufacturing by laser fusion on a metal oxides powder bed has developed considerably in the last few years and allows to produce a wide range of complex parts. The mathematical models correspond to initial boundary value problems…
We propose a framework for second-order achievability, called type deviation convergence, that is generally applicable to settings in network information theory, and is especially suitable for lossy source coding and channel coding with…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush--Kuhn--Tucker-type necessary optimality conditions in order to characterize local minimizers.…
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…
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…
This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a…
We present an algorithm for learning parametric constraints from locally-optimal demonstrations, where the cost function being optimized is uncertain to the learner. Our method uses the Karush-Kuhn-Tucker (KKT) optimality conditions of the…
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…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
In this paper, we are concerned with optimal control problems evolved on Riemannian manifolds, where the initial and final states satisfy some inequality and equality type constraints, and the control set is a separable metric space. We…
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.…
Inverse optimal control (IOC) is about estimating an unknown objective of interest given its optimal control sequence. However, truly optimal demonstrations are often difficult to obtain, e.g., due to human errors or inaccurate…
Kuhn-Tucker conditions for mathematical programming problems in Banach spaces partially ordered by cone with empty interior are obtained under strong simultaneity condition. If partial ordered cone has interior point, it is proved that…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…
In this paper, we study the perturbation analysis of a class of composite optimization problems, which is a very convenient and unified framework for developing both theoretical and algorithmic issues of constrained optimization problems.…