相关论文: A characterization of simultaneous optimization, m…
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
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…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
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…
The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…
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…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…