Related papers: Generalized Karush-Kuhn-Tucker Conditions for Real…
In this paper, we examine the problem of partial inference in the context of structured prediction. Using a generative model approach, we consider the task of maximizing a score function with unary and pairwise potentials in the space of…
This paper introduces a new method for solving quadratic programs using primal-dual interior-point methods. Instead of handling complementarity as an explicit equation in the Karush-Kuhn-Tucker (KKT) conditions, we ensure that…
Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class…
We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…
Convex separable quadratic optimization problems occur in many practical applications. In this paper, based on an iterative resolution scheme of the KKT system, we develop an efficient method for solving a quadratic programming problem with…
In this paper we consider the solvability of a non-convex regular polynomial vector optimization problem on a nonempty closed set. We introduce regularity conditions for the polynomial vector optimization problem and study properties and…
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…
We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this…
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…
Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a…