Related papers: A Non-Interior-Point Continuation Method for the O…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing…
A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed…
The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…
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…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the…
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…
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…
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high…
In this paper, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without…
In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for…
In this paper we consider constrained optimization problems where both the objective and constraint functions are of the black-box type. Furthermore, we assume that the nonlinear inequality constraints are non-relaxable, i.e. their values…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
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…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
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…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…