相关论文: A Unified Characterization of Nonlinear Scalarizin…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…
In this paper, a finite family of nonsmooth locally Lipschitz continuous functions that are invex with respect to the same function {\eta} are characterized in terms of their scalarized counterparts.
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
Motivated by resource allocation problems (RAPs) in power management applications, we investigate solutions to optimization problems that simultaneously minimize an entire class of objective functions. It is straightforward to show…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We consider the problem of classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task to find the best classifier as an optimization problem and solve…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Classical results show that gradient descent converges linearly to minimizers of smooth strongly convex functions. A natural question is whether there exists a locally nearly linearly convergent method for nonsmooth functions with quadratic…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
In this paper we maximize a class of functionals under certain constraints. We find sufficient and necessary conditions for these maximizers to exist and be unique. Moreover, we characterize them and discuss the optimality of our results by…
A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines $\displaystyle{{\left({}^{\alpha}{\mathbf B}_{i}^{k} \right)}_{i=0}^{k}}$ which depends on an index $\alpha…
This note studies numerical methods for solving compositional optimization problems, where the inner function is smooth, and the outer function is Lipschitz continuous, non-smooth, and non-convex but exhibits one of two special structures…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
We characterize the zero sets of functions in the Schur--Agler class over the unit polydisk as well as functions in the unit ball of the multiplier algebra of the Drury--Arveson space via operators associated with a unitary realization…
In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in a conlinear space. Similar results are proved for a weaker…
Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective…