Related papers: A Conditional Gradient Framework for Composite Con…
This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template…
We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…
We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
In this paper we consider a composite optimization problem that minimizes the sum of a weakly smooth function and a convex function with either a bounded domain or a uniformly convex structure. In particular, we first present a…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
We develop subgradient- and gradient-based methods for minimizing strongly convex functions under a notion which generalizes the standard Euclidean strong convexity. We propose a unifying framework for subgradient methods which yields two…
In this paper, we propose Riemannian conditional gradient methods for minimizing composite functions, i.e., those that can be expressed as the sum of a smooth function and a retraction-based convex function. We analyze the convergence of…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the…
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…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The conditional gradient method (CGM) is widely used in large-scale sparse convex optimization, having a low per iteration computational cost for structured sparse regularizers and a greedy approach to collecting nonzeros. We explore the…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…