stochastic optimization

Modified Line Search Sequential Quadratic Methods for Equality-Constrained Optimization with Unified Global and Local Convergence Guarantees

Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Other Topics Tags , ,

In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary … Read more

A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity

Categories Data Science Algorithms, Nonlinear Optimization Tags , , , ,

A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative evaluation … Read more

BattOpt: Optimal Facility Planning for Electric Vehicle Battery Recycling

Categories Energy, Global Optimization Applications, Stochastic Programming Tags , , ,

The electric vehicle (EV) battery supply chain will face challenges in sourcing scarce and expensive minerals required for manufacturing and in disposing of hazardous retired batteries. Integrating recycling technology into the supply chain has the potential to alleviate these issues; however, players in the battery market must design investment plans for recycling facilities. In this … Read more

Doubly stochastic primal dual splitting algorithm with variance reduction for saddle point problems

Categories Constrained Nonlinear Optimization, Convex Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

The structured saddle-point problem involving the infimal convolution in real Hilbert spaces finds applicability in many applied mathematics disciplines. For this purpose, we develop a stochastic primal-dual splitting algorithm with loopless variance-reduction for solving this generic problem. We first prove the weak almost sure convergence of the iterates. We then demonstrate that our algorithm achieves … Read more

Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization

Categories Constrained Nonlinear Optimization, Data Science Applications, Stochastic Programming Tags , , ,

Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been … Read more

Asynchronous Iterations in Optimization: New Sequence Results and Sharper Algorithmic Guarantees

Categories Convex Optimization, Global Optimization, Parallel Algorithms Tags , , , ,

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony impacts the convergence rates of the iterates. Our results shorten, streamline and strengthen existing convergence proofs for several asynchronous optimization … Read more

A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , ,

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth (nonconvex) optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique … Read more

Multi-model Partially Observable Markov Decision Processes

Categories Applications - OR and Management Sciences, Biomedical Applications, Stochastic Programming Tags , , ,

We propose a new multi-model partially observable Markov decision process (MPOMDP) model to address the issue of model ambiguity in partially observable Markov decision process. Here, model ambiguity is defined as the case where there are multiple credible optimization models with the same structure but different model parameters. The proposed MPOMDP model aims to learn … Read more

Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , ,

A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or … Read more

Data-Driven Stochastic Dual Dynamic Programming: Performance Guarantees and Regularization Schemes

Categories Stochastic Programming Tags , , ,

We propose a data-driven extension of the stochastic dual dynamic programming (SDDP) algorithm for multistage stochastic linear programs under a continuous-state, non-stationary Markov data process. Unlike traditional SDDP methods—which often assume a known probability distribution, stagewise independent data process, or uncertainty restricted to the right-hand side of constraints—our approach overcomes these limitations, making it more … Read more