Related papers: Exact penalty method for D-stationary point of non…
We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…
We introduce a novel method for handling endpoint constraints in constrained differential dynamic programming (DDP). Unlike existing approaches, our method guarantees quadratic convergence and is exact, effectively managing rank…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is…
Quadratically constrained quadratic programs (QCQPs) have a wide range of applications in signal processing and wireless communications. Non-convex QCQPs are NP-hard in general. Existing approaches relax the non-convexity using…
Change point analysis is concerned with detecting and locating structure breaks in the underlying model of a sequence of observations ordered by time, space or other variables. A widely adopted approach for change point analysis is to…
The goal of this article is to study necessary and sufficient conditions for the exactness of penalty functions and the existence of global saddle points of augmented Lagrangians for well-posed (in a suitable sense) constrained optimization…
We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem. We first show that, unlike the gradient descent method for unconstrained optimization, the vanilla projected…
Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed…
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…
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…
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…
We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via…
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…
We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality…
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…