Related papers: A Sequential Homotopy Method for Mathematical Prog…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
The primal--dual hybrid gradient method (PDHGM, also known as the Chambolle--Pock method) has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems. In this…
This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We study single-loop gradient-flow dynamics for nested optimization, where the outer variable evolves while auxiliary variables track the inner solution map. While existing analyses typically rely on problem- and condition-specific Lyapunov…
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…