Related papers: Convex Relaxations for Subset Selection
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…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex…
The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
In this work, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semi-blind signal recovery from non-ideal channels. We develop numerical algorithms based on convex optimization…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility…
We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman operators preserve convexity. In addition to a theoretical…
We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
This paper investigates recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are non-convex optimization problems in general, and…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…