Related papers: A constrained tropical optimization problem: compl…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an…
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…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility…
A linear vector equation in two unknown vectors is examined in the framework of tropical algebra dealing with the theory and applications of semirings and semifields with idempotent addition. We consider a two-sided equation where each side…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…
For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
In this paper, we present an optimization based method for path planning of a mobile robot subject to time bounded temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specification such as…
Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable…
In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…