Related papers: Automatic Generation of Explicit Quadratic Program…
We study a multi-period convex quadratic optimization problem, where the state evolves dynamically as an affine function of the state, control, and indicator variables in each period. We begin by projecting out the state variables using…
In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose…
A commonly occurring computation idiom in neural networks is to perform some pointwise operations on the result of a matrix multiplication. Such a sequence of operations is typically represented as a computation graph in deep learning…
Given symmetric matrices $A_0, A_1, \ldots, A_n$ of size $m$ with rational entries, the set of real vectors $x = (x_1, \ldots, x_n)$ such that the matrix $A_0 + x_1 A_1 + \cdots + x_n A_n$ has non-negative eigenvalues is called a…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…