Related papers: Primal superlinear convergence of SQP methods in p…
Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to…
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…
We prove that a "first-order" Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/\kappa_R)^k$, where $\kappa_R$ is the condition number of the Riemannian…
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…
We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an $L^2$ neighborhood of a local solution that satisfies no-gap second-order sufficient…
We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton updates on both the primal and dual variables of the…
We address the slow convergence and poor stability of quasi-newton sequential quadratic programming (SQP) methods that is observed when solving experimental design problems, in particular when they are large. Our findings suggest that this…
The combination of nonlinear FETI-DP (Dual Primal Finite Element Tearing and Interconnecting) and Quasi-Newton methods using a sequential quadratic programming (SQP) approach is considered. Nonlinear FETI-DP methods are parallel iterative…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…
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…
Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and…
We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation,…
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…