Related papers: Projections onto the canonical simplex with additi…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We consider the minimum distance projection in the $L_2$-norm from an arbitrary point in an $n$-dimensional, Euclidian space onto the canonical simplex. It is shown that this problem reduces to a univariate problem that can be solved by a…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…