Related papers: Optimality Conditions for Cardinality-Constrained …
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…
We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming…
We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global…
A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client…
We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee…
In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind of problem is generally difficult to deal with, because it involves a constraint that is not continuous…
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse…
In this paper, we aim at solving the cardinality constrained high-order portfolio optimization, i.e., mean-variance-skewness-kurtosis model with cardinality constraint (MVSKC). Optimization for the MVSKC model is of great difficulty in two…
Cardinality-constrained optimization (CCO) is a popular topic in sparse learning and signal recovery, yet remains challenging due to the inherent nonconvexity and discontinuity of cardinality constraints. This paper investigates the exact…
Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or…
In this paper, we consider the cardinality-constrained optimization problems and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…
Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality…
This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by…
A lot of problems, from fields like sparse signal processing, statistics, portfolio selection, and machine learning, can be formulated as a cardinality constraint optimization problem. The cardinality constraint gives the problem a discrete…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
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…