Related papers: A second-order sequential optimality condition for…
This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is countably $PC^2$ (continuous and $C^2$ apart from countably many points). We…
This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus…
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…
Direct collocation for Bolza optimal control yields discrete Karush-Kuhn-Tucker (KKT) points, while practical solvers expose only discrete quantities such as primal-dual iterates, reduced Hessians, and Jacobians. This creates a gap between…
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this…
There are several concepts and definitions that characterize and give optimality conditions for solutions of a vector optimization problem. One of the most important is the first-order necessary optimality condition that generalizes the…
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…
Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear…
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…
We present a unified study of first and second order necessary and sufficient optimality conditions for minimax and Chebyshev optimisation problems with cone constraints. First order optimality conditions for such problems can be formulated…
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…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee…
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…
Among many approaches to increase the computational efficiency of semidefinite programming (SDP) relaxation for quadratic constrained quadratic programming problems (QCQPs), exploiting the aggregate sparsity of the data matrices in the SDP…
A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the…
In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…
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.…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…