相关论文: New merit functions for multiobjective optimizatio…

The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…

We examine a new optimization problem formulated in the tropical mathematics setting as a further extension of certain known problems. The problem is to minimize a nonlinear objective function, which is defined on vectors over an idempotent…

Architecture optimization is the process of automatically generating design options, typically to enhance software's quantifiable quality attributes, such as performance and reliability. Multi-objective optimization approaches have been…

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…

Using the Fitzpatrick function, we characterize the solutions for different classes of deterministic and stochastic differential equations driven by maximal monotone operators (or in particular subdifferential operators) as the minimum…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…

In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved…

We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest…

Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…

Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations…

Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…

Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…

Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…

The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust…

Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…

A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…