Related papers: Convexification Techniques for Fractional Programs
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…
In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
We propose a solution approach for the problem (P) of minimizing an unconstrained binary polynomial optimization problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The…
Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…
In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs. We propose two types of bounds for quadratically constrained quadratic programs, quadratic and cubic bounds. For quadratic bounds, we use affine…
Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We…
In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized…
In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems…
In this paper, we present a novel approach to decompose a given piecewise affine (PWA) function into two convex PWA functions. Convex decompositions are useful to speed up or distribute evaluations of PWA functions. Different approaches to…
This paper presents a canonical dual approach to the problem of minimizing the sum of a quadratic function and the ratio of nonconvex function and quadratic functions, which is a type of non-convex optimization problem subject to an…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
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…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…