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Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

Point sets matching method is very important in computer vision, feature extraction, fingerprint matching, motion estimation and so on. This paper proposes a robust point sets matching method. We present an iterative algorithm that is…

Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…

In this paper, we present an interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which we propose a generalization of the work of Kheirfam and Nasrollahi…

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

Image matting is a fundamental computer vision problem and has many applications. Previous algorithms have poor performance when an image has similar foreground and background colors or complicated textures. The main reasons are prior…

We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…

In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

We study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to…

The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…