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Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual…
The uniform quadratic optimizatin problem (UQ) is a nonconvex quadratic constrained quadratic programming (QCQP) sharing the same Hessian matrix. Based on the second-order cone programming (SOCP) relaxation, we establish a new sufficient…
Complex system design problems, such as those involved in aerospace engineering, require the use of numerically costly simulation codes in order to predict the performance of the system to be designed. In this context, these codes are often…
Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…
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…
In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…
Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…
In pursuit of enhancing the comprehensive efficiency of production systems, our study focused on the joint optimization problem of scheduling and machine maintenance in scenarios where product rework occurs. The primary challenge lies in…
Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…
Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
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…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…