Related papers: Minima distribution for global optimization

Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…

Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic…

We prove that the smallest minimizer s(f) of a real convex function f is less than or equal to a real point x if and only if the right derivative of f at x is non-negative. Similarly, the largest minimizer t(f) is greater or equal to x if…

The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…

In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…

Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this work, we give an exact characterization of the set of possible minimizers of the sum. Our results…

In the present work we study a problem of finding a global minimum of a piecewise affine function. We employ optimality conditions for the problem in terms of coexhausters and use them to state and prove necessary and sufficient conditions…

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…

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 extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator.…

We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…

Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…