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In the present paper, several types of efficiency conditions are established for vector optimization problems with cone constraints affected by uncertainty, but with no information of stochastic nature about the uncertain data. Following a…

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…

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…

Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic…

Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…

Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy…

Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired…

We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…

This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…

We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…

Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to…

The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…

In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…

Recently the shape-restricted inference has gained popularity in statistical and econometric literature in order to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect…

Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…

We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as…

Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…