Related papers: KKT Conditions, First-Order and Second-Order Optim…
Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…
We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…
This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…
This paper introduces a novel approach to contextual stochastic optimization, integrating operations research and machine learning to address decision-making under uncertainty. Traditional methods often fail to leverage contextual…
In this paper, we provide a complete characterization on the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for convex constrained optimization problems regularized by the nuclear norm function. This study is…
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…
We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any…
We provide an exact analysis of a class of randomized algorithms for solving overdetermined least-squares problems. We consider first-order methods, where the gradients are pre-conditioned by an approximation of the Hessian, based on a…
Performance indicators are essential tools for assessing the convergence behavior of multi-objective optimization algorithms, particularly when the true Pareto front is unknown or difficult to approximate. Classical reference-based metrics…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
We study distributed optimization problems when $N$ nodes minimize the sum of their individual costs subject to a common vector variable. The costs are convex, have Lipschitz continuous gradient (with constant $L$), and bounded gradient. We…
We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with…
In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
In this article we consider a convex feasible set described by inequality constraints that are continuous and not necessarily Lipschitz or convex. We show that if the Slater constraint qualification and a non-degeneracy condition are…
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…