Related papers: On the Stationary Duality of Structural Composite …
In this paper, we propose a robust optimization-based heuristic algorithm for the chance-constrained binary knapsack problem (CKP). We assume that the weights of items are independent normally distributed. By utilizing the properties of the…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits…
Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and…
A distributed nonsmooth robust resource allocation problem with cardinality constrained uncertainty is investigated in this paper. The global objective is consisted of local objectives, which are convex but nonsmooth. Each agent is…
Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
In this paper we propose an Approximate Weak stationarity ($AW$-stationarity) concept designed to deal with {\em Mathematical Programs with Cardinality Constraints} (MPCaC), and we proved that it is a legitimate optimality condition…
The main goal of this paper is to relate the topologically relevant stationary points of a cardinality-constrained optimization problem and its continuous reformulation up to their type. For that, we focus on the nondegenerate M- and…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Topology optimization for general materials is correctly formulated as a bi-level knapsack problem, which is considered to be NP-hard in global optimization and computer science. By using canonical duality theory (CDT) developed by the…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Many important collective decision-making problems can be seen as multi-agent versions of discrete optimisation problems. Participatory budgeting, for instance, is the collective version of the knapsack problem; other examples include…
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting…