Related papers: Optimality Conditions for Cardinality-Constrained …
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment or blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale…
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
In the practical business environment, portfolio managers often face business-driven requirements that limit the number of constituents in their tracking portfolio. A natural index tracking model is thus to minimize a tracking error measure…
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…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
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…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are…
We consider optimal allocation problems with Conditional Value-At-Risk (CVaR) constraint. We prove, under very mild assumptions, the convergence of the Sample Average Approximation method (SAA) applied to this problem, and we also exhibit a…