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We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content…
Tensor completion is a technique of filling missing elements of the incomplete data tensors. It being actively studied based on the convex optimization scheme such as nuclear-norm minimization. When given data tensors include some noises,…
Various post-training uniform quantization methods have usually been studied based on convex optimization. As a result, most previous ones rely on the quantization error minimization and/or quadratic approximations. Such approaches are…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
We consider a class of optimization problems with Cartesian variational inequality (CVI) constraints, where the objective function is convex and the CVI is associated with a monotone mapping and a convex Cartesian product set. This…
K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
In this paper, we mainly study solution uniqueness of some convex optimization problems. Our characterizations of solution uniqueness are in terms of the radial cone. This approach allows us to know when a unique solution is a strong…