Related papers: An interior point method for nonlinear optimizatio…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the…
In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible…
Due to critical environmental issues, the power systems have to accommodate a significant level of penetration of renewable generation which requires smart approaches to the power grid control. Associated optimal control problems are…
A trajectory-following primal--dual interior-point method solves nonlinear optimization problems with inequality and equality constraints by approximately finding points satisfying perturbed Karush--Kuhn--Tucker optimality conditions for a…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs with general equality and…
Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
We propose a primal-dual interior-point method (IPM) with convergence to second-order stationary points (SOSPs) of nonlinear semidefinite optimization problems, abbreviated as NSDPs. As far as we know, the current algorithms for NSDPs only…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
In this work, the joint use of a mixed penalty-interior point method and direct search is proposed, to address {nonlinear} constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…
Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…
This paper presents an interior point method for pure-state and mixed-constrained optimal control problems for dynamics, mixed constraints, and cost function all affine in the control variable. This method relies on resolving a sequence of…