相关论文: Finding quadratic underestimators for optimal valu…

This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…

We consider optimization problems of the first eigenvalue of elliptic operators with applications to two-phase optimal design problems (also known as topology optimization problems) of conductivity and elasticity relaxed by homogenization.…

Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems. In a QCQP, we are asked to minimize a (possibly nonconvex) quadratic function subject to a number of (possibly nonconvex) quadratic…

The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…

Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with…

Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…

Modern second order solvers for convex optimisation, such as interior point methods, rely on primal dual information and are difficult to warm start, limiting their applicability in real time control. We propose the PVM, a duality free…

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…

The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem…

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…

Joint radar receive filter and waveform design is non-convex, but is individually convex for a fixed receiver filter while optimizing the waveform, and vice versa. Such classes of problems are fre- quently encountered in optimization, and…

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…

We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…

This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.

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…

This work puts forward a form finding problem of designing a least-volume vault that is a surface structure spanning over a plane region, which via pure compression transfers a vertically tracking load to the supporting boundary. Through a…

A geometric nonconvex conic optimization problem (COP) was recently proposed by Kim, Kojima and Toh as a unified framework for convex conic reformulation of a class of quadratic optimization problems and polynomial optimization problems.…

For nonconvex quadratically constrained quadratic programs (QCQPs), we first show that, under certain feasibility conditions, the standard semidefinite (SDP) relaxation is exact for QCQPs with bipartite graph structures. The exact optimal…

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…

In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…