Related papers: A survey of hidden convex optimization
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…