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The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Preliminary results of our investigations on solving indefinite qua\-dra\-tic programs by dynamical systems are given. First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…
In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a point, and (iii) deciding…