Related papers: On Subdifferentials Via a Generalized Conjugation …
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via…
Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue.…
Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function.…
The $\epsilon$-subdifferential of convex univariate piecewise linear-quadratic functions can be computed in linear worst-case time complexity as the level-set of a convex function. Using dichotomic search, we show how the computation can be…
The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the…
Weak sharp minimality is a notion emerged in optimization, whose utility is largeley recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behaviour of such problems.…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
Hermite subdivision schemes act on vector valued data that is not only considered as functions values in $\mathbb{R}^r$, but as consecutive derivatives, which leads to a mild form of level dependence of the scheme. Previously, we have…
In this paper, we propose a clean and general proof framework to establish the convergence analysis of the Difference-of-Convex (DC) programming algorithm (DCA) for both standard DC program and convex constrained DC program. We first…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
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…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
In this paper, we introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper extended real function. This derivative is harmonized with the classical higher-order Fr\'echet…
As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage…
Given an algebra $A$ over a differential field $K$, we study derivations on $A$ that are compatible with the derivation on $K$. There is a universal object, which is a twisted version of the usual module of differentials, and we establish…