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In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of…
Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our methods are particularly well suited for convex quadratic programming problems…
In this paper, we propose a new primal-dual algorithm for minimizing $f(x) + g(x) + h(Ax)$, where $f$, $g$, and $h$ are proper lower semi-continuous convex functions, $f$ is differentiable with a Lipschitz continuous gradient, and $A$ is a…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
This paper proposes an efficient hypergraph partitioning framework based on a novel multi-objective non-convex constrained relaxation model. A modified accelerated proximal gradient algorithm is employed to generate diverse $k$-dimensional…
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 dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
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…
In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…