相关论文: Uncomputability of Global Optima for Nonconvex Fun…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
Non-convex optimization problems can be approximately solved via relaxation or local algorithms. For many practical problems such as optimal power flow (OPF) problems, both approaches tend to succeed in the sense that relaxation is usually…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our…
We present results on the estimation and evaluation of success probabilities for ordinal optimisation over uncountable sets (such as subsets of $\mathbb{R}^{d}$). Our formulation invokes an assumption of a Gaussian copula model, and we show…
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…
The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is…
We note that known methods achieving the optimal oracle complexity for first order convex optimization require quadratic memory, and ask whether this is necessary, and more broadly seek to characterize the minimax number of first order…
The classical algorithms for online learning and decision-making have the benefit of achieving the optimal performance guarantees, but suffer from computational complexity limitations when implemented at scale. More recent sophisticated…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the…
For a matrix $W \in \mathbb{Z}^{m \times n}$, $m \leq n$, and a convex function $g: \mathbb{R}^m \rightarrow \mathbb{R}$, we are interested in minimizing $f(x) = g(Wx)$ over the set $\{0,1\}^n$. We will study separable convex functions and…
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…
The global optimization have the very extensive applications in econometrics, science and engineering. However, the global optimization for non-convex objective functions is particularly difficult since most of the existing global…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In compressed sensing a sparse vector is approximately retrieved from an under-determined equation system $Ax=b$. Exact retrieval would mean solving a large combinatorial problem which is well known to be NP-hard. For $b$ of the form…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an…
We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…