Related papers: Spectrahedral Regression
To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
We present a hierarchy of semidefinite programs (SDPs) for the problem of fitting a shape-constrained (multivariate) polynomial to noisy evaluations of an unknown shape-constrained function. These shape constraints include convexity or…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
Seminal work by Edmonds and Lovasz shows the strong connection between submodularity and convexity. Submodular functions have tight modular lower bounds, and subdifferentials in a manner akin to convex functions. They also admit poly-time…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
We consider strongly convex-concave minimax problems in the federated setting, where the communication constraint is the main bottleneck. When clients are arbitrarily heterogeneous, a simple Minibatch Mirror-prox achieves the best…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…