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Frontal photopolymerization (FPP) provides a versatile method for the rapid fabrication of solid polymer network materials by exposing photosensitive molecules to light. Dimensional control of structures created by this process is crucial…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
Polynomial optimization problems often arise in sequences indexed by dimension, and it is of interest to compute bounds on the optimal values of all problems in the sequence. Examples include certifying inequalities between symmetric…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
In this paper we consider the solvability of a non-convex regular polynomial vector optimization problem on a nonempty closed set. We introduce regularity conditions for the polynomial vector optimization problem and study properties and…
In this paper, we study the problem of minimizing a sum of convex objective functions, which are locally available to agents in a network. Distributed optimization algorithms make it possible for the agents to cooperatively solve the…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.).…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…