Related papers: A symbolic algorithm for exact polynomial optimiza…
We introduce a new non-degeneracy condition at infinity for a real or a mixed polynomial mapping $F$ which allows us to approximate its bifurcation locus in terms of certain Newton polyhedra. We derive a sufficiency result for the Jacobian…
We consider the problem of planning with participation constraints introduced in [Zhang et al., 2022]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
This article considers the problem of solving a system of $n$ real polynomial equations in $n+1$ variables. We propose an algorithm based on Newton's method and subdivision for this problem. Our algorithm is intended only for nondegenerate…
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…
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider an optimization problem in a convex space $E$ with an affine objective function, subject to $J$ constraints in the forms of inequalities on some other affine functions, where $J$ is a given nonnegative integer. Under suitable…
The object of investigation in this paper are vector nonlinear programming problems with cone constraints. We introduce the notion of a Fritz John pseudoinvex cone-constrained vector problem. We prove that a problem with cone constraints is…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…
We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form…
We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition number minimization problem, under structured transformations…