Related papers: On Subdifferentials Via a Generalized Conjugation …
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…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
In this article, we study $gH$-subdifferential calculus of convex interval-valued functions (IVFs) and apply it in a nonconvex composite model of interval optimization problems (IOPs). It is found that the $gH$-directional derivative of…
Separability of multivariate functions alleviates the difficulty in finding a minimum or maximum value of a function such that an optimal solution can be searched by solving several disjoint problems with lower dimensionalities. In most of…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
This paper proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the average of…
A wide range of optimization problems can often be written in terms of generalized convex functions (GCFs). When this structure is present, it can convert certain nested bilevel objectives into single-level problems amenable to standard…
In this paper, we deal with constraint qualifications, the stationary concept and the optimality conditions for nonsmooth mathematical programs with equilibrium constraints. The main tool of our study is the notion of tangential…
We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…
We establish explicit data-dependent and symmetric characterizations of the subdifferential of the supremum of convex functions, formulated directly in terms of the underlying data functions. In our approach, both active and non-active…
Demixing is the problem of identifying multiple structured signals from a superimposed observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. We present a new solution to determine…
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…
General distribution steering is intrinsically an infinite-dimensional problem, when the continuous distributions to steer are arbitrary. We put forward a moment representation of the primal system for control in [42]. However, the system…
This work provides calculus for the Fr\'echet and limiting subdifferential of the pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start our study showing fuzzy results about the Fr\'echet…
Cartesian reverse derivative categories (CRDCs) provide an axiomatic generalization of the reverse derivative, which allows generalized analogues of classic optimization algorithms such as gradient descent to be applied to a broad class of…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a locally convex space, to be Lipschitz continuous. Our criterion relies on the intersections of the "epsilon-subdifferentials of…
We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed…
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…