Related papers: Applications of Convex Analysis within Mathematics
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator…
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 study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We also investigate under…
We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Amp\`ere measures. As an application, we give a new…
Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood…
Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In doing…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…
Monotone convex operators and time-consistent systems of operators appear naturally in stochastic optimization and mathematical finance in the context of pricing and risk measurement. We study the dual representation of a monotone convex…
This paper consists of four general parts: convex sets; convex functions; convex optimization; and the interior-point algorithm. I will start by introducing the definition of convex sets and give three common convex set examples which will…