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This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
Optimization is offered as an objective approach to resolving complex, real-world decisions involving uncertainty and conflicting interests. It drives business strategies as well as public policies and, increasingly, lies at the heart of…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
As researchers and practitioners of applied machine learning, we are given a set of requirements on the problem to be solved, the plausibly obtainable data, and the computational resources available. We aim to find (within those bounds)…
A re-calibration is proposed for "numerical analysis" as it arises specifically within the broader, embracing field of modern computer science (CS). This would facilitate research into theoretical and practicable models of real-number…
Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…
By virtue of its great utility in solving real-world problems, optimization modeling has been widely employed for optimal decision-making across various sectors, but it requires substantial expertise from operations research professionals.…
Access to healthcare facilities is a critical issue in developing countries, where limited resources and significant challenges hinder progress toward universal health coverage, one of the targets pursued by the United Nations. As a result,…
quest for processing speed potential. In fact, we always get a fraction of the technically available computing power (so-called {\em theoretical peak}), and the gap is likely to go hand-to-hand with the hardware complexity of the target…
Optimization is used extensively in engineering, industry, and finance, and various methods are used to transform problems to the point where they are amenable to solution by numerical methods. We describe progress towards developing a…
Clinical trials are pivotal in the drug discovery process to determine the safety and efficacy of a drug candidate. The high failure rates of these trials are attributed to deficiencies in clinical model development and protocol design.…
Optimization has been becoming a central of studies in mathematic and has many areas with different applications. However, many themes of optimization came from different area have not ties closing to origin concepts. This paper is to…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to…
Solving optimization problems with parallel algorithms has a long tradition in OR. Its future relevance for solving hard optimization problems in many fields, including finance, logistics, production and design, is leveraged through the…
Decentralized optimization enables multiple devices to learn a global machine learning model while each individual device only has access to its local dataset. By avoiding the need for training data to leave individual users' devices, it…
Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this…