Related papers: On the structure of optimal solutions in a mathema…
We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…
We consider the minimization or maximization of the $J$th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix Anal. Appl., 35, 699-724). This work addresses the setting…
In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and…
We study weighted Sobolev inequalities on open convex cones endowed with $\alpha$-homogeneous weights satisfying a certain concavity condition. We establish a so-called reduction principle for these inequalities and characterize optimal…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…
We consider the convex optimization problem P: min {f(x): x in K} where "f" is convex continuously differentiable, and K is a compact convex set in Rn with representation {x: g_j(x) >=0, j=1,;;,m} for some continuously differentiable…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity…
The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
We develop refined Karush-Kuhn-Tucker (KKT) and Fritz-John (FJ)-type optimality conditions for nonsmooth, nonconvex mathematical pro\-gra\-mming problems. We pay special attention in the case that the functional constraint belongs to a…
In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We…