Related papers: Existence of Weak Efficient Solutions of Set-Value…

The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…

This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized vector…

To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…

In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum…

In this work, we study the external and internal stability of minimal solutions to set-valued optimization problems in a new functional framework. We consider perturbations on both the objective function and the admissible domain. To…

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

Weakly-supervised object localization (WSOL) enables finding an object using a dataset without any localization information. By simply training a classification model using only image-level annotations, the feature map of the model can be…

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to…

This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…

Rank-constrained optimization problems have received an increasing intensity of interest recently, because many optimization problems in communications and signal processing applications can be cast into a rank-constrained optimization…

Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…

The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint sets. The main attention is paid to the two major…

Our aim in this article is two-fold. We use the Charnes-Cooper scalarization technique to develop KKT type conditions to completely characterize Pareto minimizers of convex vector optimization problems and further, we use that scalarization…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

Set-valued prediction is a well-known concept in multi-class classification. When a classifier is uncertain about the class label for a test instance, it can predict a set of classes instead of a single class. In this paper, we focus on…

We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…

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…

We present a theorem of Sard type for semi-algebraic set-valued mappings whose graphs have dimension no larger than that of their range space: the inverse of such a mapping admits a single-valued analytic localization around any pair in the…