Related papers: Semi-infinite optimization with sums of exponentia…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
In this paper, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when $\ell_0$-penalized models are fitted and usually lead to NP-Hard…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
The sum of ratios problem has a variety of important applications in economics and management science, but it is difficult to globally solve this problem. In this paper, we consider the minimization problem of a sum of a number of…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…